In this paper,the authors derive H¨older gradient estimates for graphic functions of minimal graphs of arbitrary codimensions over bounded open sets of Euclidean space under some suitable conditions.
We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the...We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.展开更多
An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary ...An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.展开更多
In this paper,we consider the pointwise boundary Lipschitz regularity of solutions for the semilinear elliptic equations in divergence form mainly under some weaker assumptions on nonhomogeneous term and the boundary....In this paper,we consider the pointwise boundary Lipschitz regularity of solutions for the semilinear elliptic equations in divergence form mainly under some weaker assumptions on nonhomogeneous term and the boundary.If the domain satisfies C1,Dinicondition at a boundary point,and the nonhomogeneous term satisfies Dini continuity condition and Lipschitz Newtonian potential condition,then the solution is Lipschitz continuous at this point.Furthermore,we generalize this result to Reifenberg C1,Dinidomains.展开更多
The distributed source boundary point method (DSBPM) is used as the spatial transform algorithm for realizing nearfield acoustic holography (NAH), the sensitivity of the reconstructed solution to the measurement e...The distributed source boundary point method (DSBPM) is used as the spatial transform algorithm for realizing nearfield acoustic holography (NAH), the sensitivity of the reconstructed solution to the measurement errors is analyzed, and the regularization method is proposed to stabilize the reconstruction process, control the influence of the measurement errors and get a better approximate solution. An oscillating sphere is investigated as a numerical example, the influence of the measurement errors on the reconstruction solution is demonstrated, and the feasibility and validity of the regularization method are validated. Key words: Acoustic holography Boundary point method Inverse problem Regularization展开更多
In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the dire...In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.展开更多
In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result si...In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result similar to L q-theory for the one with Dirichlet boundary condition is obtained. Using the result, for the steady Navier-Stokes equations we obtain regularity as the case of Dirichlet boundary conditions. Furthermore,for the time-dependent 2-D Navier-Stokes equations we prove uniqueness and existence of regular solutions,which is similar to J.M.Bernard's results[6]for the time-dependent 2-D Stokes equations.展开更多
The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixe...The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.展开更多
For the birth–death Q-matrix with regular boundary,its minimal process and its maximal process are closely related.In this paper,we obtain the uniform decay rate and the quasi-stationary distribution for the minimal ...For the birth–death Q-matrix with regular boundary,its minimal process and its maximal process are closely related.In this paper,we obtain the uniform decay rate and the quasi-stationary distribution for the minimal process.And via the construction theory,we mainly derive the eigentime identity and the distribution of the fastest strong stationary time(FSST)for the maximal process.展开更多
In this paper, the authors will apply De Giorgi-Nash-Moser iteration to establish boundary H?lder estimates for a class of degenerate elliptic equations in piecewise C^(2)-smooth domains.
The authors study the continuity estimate of the solutions of almost harmonic maps with the perturbation term f in a critical integrability class(Zygmund class)L^(n/2)log^(q) L,n is the dimension with n≥3.They prove ...The authors study the continuity estimate of the solutions of almost harmonic maps with the perturbation term f in a critical integrability class(Zygmund class)L^(n/2)log^(q) L,n is the dimension with n≥3.They prove that when q>n/2 the solution must be continuous and they can get continuity modulus estimates.As a byproduct of their method,they also study boundary continuity for the almost harmonic maps in high dimension.展开更多
Due to the high accuracy and fast acquisition speed offered by airborne Light Detection and Ranging(LiDAR)technology,airborne LiDAR point clouds have been widely used in three-dimensional building model reconstruction...Due to the high accuracy and fast acquisition speed offered by airborne Light Detection and Ranging(LiDAR)technology,airborne LiDAR point clouds have been widely used in three-dimensional building model reconstruction.This paper presents a novel approach to segment building roofs from point clouds using a Gaussian mixture model in which buildings are represented by a mixture of Gaussians(MoG).The Expectation-Maximization(EM)algorithm with the minimum description length(MDL)principle is employed to obtain the optimal parameters of the MoG model for separating building roofs.To separate complete planar building roofs,coplanar Gaussian components are merged according to their distances to the corresponding planes.In addition,shape analysis is utilized to remove nonplanar objects caused by trees and irregular artifacts.Building models are obtained by combining segmented planar roofs,topological relationships,and regularized building boundaries.Roof intersection segments and points are derived by the segmentation results,and a rasterbased regularization method is employed to obtain geometrically correct and regular building models.Experimental results suggest that the segmentation method is able to separate building roofs with high accuracy while maintaining correct topological relationships among roofs.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11871156,11922106,11531012)。
文摘In this paper,the authors derive H¨older gradient estimates for graphic functions of minimal graphs of arbitrary codimensions over bounded open sets of Euclidean space under some suitable conditions.
基金Supported by NSF(No. 10531020) of Chinathe Program of 985 Innovation Engineering on Information in Xiamen University (2004-2007) and NCETXMU
文摘We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.
文摘An improved version of the regular boundary element method, the artificial boundary node approach, is derived. A simple contact algorithm is designed and implemented into the direct boundary element, regular boundary element and artificial boundary node approaches. The exisiting and derived approaches are tested using some case studies. The results of the artificial boundary node approach are compared with those of the existing boundary element program, the regular element approach, ANSYS and analytical solution whenever possible. The results show the effectiveness of the artificial boundary node approach for a wider range of boundary offsets.
基金The third author was partially supported by NSFC(Grant Nos.11771285 and 12031012)。
文摘In this paper,we consider the pointwise boundary Lipschitz regularity of solutions for the semilinear elliptic equations in divergence form mainly under some weaker assumptions on nonhomogeneous term and the boundary.If the domain satisfies C1,Dinicondition at a boundary point,and the nonhomogeneous term satisfies Dini continuity condition and Lipschitz Newtonian potential condition,then the solution is Lipschitz continuous at this point.Furthermore,we generalize this result to Reifenberg C1,Dinidomains.
基金This project is supported by National Natural Science Foundation of China(No.50275044)Research Fund for Doctoral Program of Ministry of Education of China(No.20020359005).
文摘The distributed source boundary point method (DSBPM) is used as the spatial transform algorithm for realizing nearfield acoustic holography (NAH), the sensitivity of the reconstructed solution to the measurement errors is analyzed, and the regularization method is proposed to stabilize the reconstruction process, control the influence of the measurement errors and get a better approximate solution. An oscillating sphere is investigated as a numerical example, the influence of the measurement errors on the reconstruction solution is demonstrated, and the feasibility and validity of the regularization method are validated. Key words: Acoustic holography Boundary point method Inverse problem Regularization
基金The financial support provided from the Ministry of Science and Technology of Taiwan is greatly appreciated by the authors(MOST 108-2221-E-006-186).
文摘In engineering practice,analysis of interfacial thermal stresses in composites is a crucial task for assuring structural integrity when sever environmental temperature changes under operations.In this article,the directly transformed boundary integrals presented previously for treating generally anisotropic thermoelasticity in two-dimension are fully regularized by a semi-analytical approach for modeling thin multi-layers of anisotropic/isotropic composites,subjected to general thermal loads with boundary conditions prescribed.In this process,an additional difficulty,not reported in the literature,arises due to rapid fluctuation of an integrand in the directly transformed boundary integral equation.In conventional analysis,thin adhesives are usually neglected due to modeling difficulties.A major concern arises regarding the modeling error caused by such negligence of the thin adhesives.For investigating the effect of the thin adhesives considered,the regularized integral equation is applied for analyzing interfacial stresses in multiply bonded composites when thin adhesives are considered.Since all integrals are completely regularized,very accurate integration values can be still obtained no matter how the source point is close to the integration element.Comparisons are made for some examples when the thin adhesives are considered or neglected.Truly,this regularization task has laid sound fundamentals for the boundary element method to efficiently analyze the interfacial thermal stresses in 2D thin multiply bonded anisotropic composites.
基金Supported by TWAS,UNESCO and AMSS in Chinese Academy of Sciences
文摘In this paper we are concerned with the regularity of solutions to the Navier-Stokes equations with the condition on the pressure on parts of the boundary where there is flow. For the steady Stokes problem a result similar to L q-theory for the one with Dirichlet boundary condition is obtained. Using the result, for the steady Navier-Stokes equations we obtain regularity as the case of Dirichlet boundary conditions. Furthermore,for the time-dependent 2-D Navier-Stokes equations we prove uniqueness and existence of regular solutions,which is similar to J.M.Bernard's results[6]for the time-dependent 2-D Stokes equations.
基金Supported by the National Basic Research Program of China(973 Program)(No.2012CB025904)the National Natural Science Foundation of China(No.90916027)
文摘The global boundness and existence are presented for the kind of the Rosseland equation with a general growth condition. A linearized map in a closed convex set is defined. The image set is precompact, and thus a fixed point exists. A multi-scale expansion method is used to obtain the homogenized equation. This equation satisfies a similar growth condition.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11501531,11701265,11771047)。
文摘For the birth–death Q-matrix with regular boundary,its minimal process and its maximal process are closely related.In this paper,we obtain the uniform decay rate and the quasi-stationary distribution for the minimal process.And via the construction theory,we mainly derive the eigentime identity and the distribution of the fastest strong stationary time(FSST)for the maximal process.
基金supported by the National Natural Science Foundation of China(Nos.11631011,11871160,12141105)。
文摘In this paper, the authors will apply De Giorgi-Nash-Moser iteration to establish boundary H?lder estimates for a class of degenerate elliptic equations in piecewise C^(2)-smooth domains.
文摘The authors study the continuity estimate of the solutions of almost harmonic maps with the perturbation term f in a critical integrability class(Zygmund class)L^(n/2)log^(q) L,n is the dimension with n≥3.They prove that when q>n/2 the solution must be continuous and they can get continuity modulus estimates.As a byproduct of their method,they also study boundary continuity for the almost harmonic maps in high dimension.
基金This work was supported by the National Key Scientific Instrument and Equipment Development Projects of China[grant number 2013YQ120343]the National Natural Science Foundation of China[grant numbers 41171265 and 41101436]the 100 Talents Program of the Chinese Academy of Sciences.
文摘Due to the high accuracy and fast acquisition speed offered by airborne Light Detection and Ranging(LiDAR)technology,airborne LiDAR point clouds have been widely used in three-dimensional building model reconstruction.This paper presents a novel approach to segment building roofs from point clouds using a Gaussian mixture model in which buildings are represented by a mixture of Gaussians(MoG).The Expectation-Maximization(EM)algorithm with the minimum description length(MDL)principle is employed to obtain the optimal parameters of the MoG model for separating building roofs.To separate complete planar building roofs,coplanar Gaussian components are merged according to their distances to the corresponding planes.In addition,shape analysis is utilized to remove nonplanar objects caused by trees and irregular artifacts.Building models are obtained by combining segmented planar roofs,topological relationships,and regularized building boundaries.Roof intersection segments and points are derived by the segmentation results,and a rasterbased regularization method is employed to obtain geometrically correct and regular building models.Experimental results suggest that the segmentation method is able to separate building roofs with high accuracy while maintaining correct topological relationships among roofs.