We prove the existence of a positive solution to the problem-Δu=a(x)f(u), x∈Ω, u(x)=0,x∈Ω,where Ω is a bounded domain in R n with smooth boundary, a(x) is allowed to change sign.
Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this pap...Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems.展开更多
In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certa...In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.展开更多
The singularly perturbed problems for the nonlinear elliptic systems in the half space are considered. Under suitable conditions, using the comparison theorem the existence and asymptotic behavior of solution for the ...The singularly perturbed problems for the nonlinear elliptic systems in the half space are considered. Under suitable conditions, using the comparison theorem the existence and asymptotic behavior of solution for the boundary value problem are studied.展开更多
In this paper, the author studies the regularity of solutions to the Dirichlet problem forequation Lu = f, where L is a second order degenerate elliptic operator in divergence form inΩ, a bounded open subset of Rn (n...In this paper, the author studies the regularity of solutions to the Dirichlet problem forequation Lu = f, where L is a second order degenerate elliptic operator in divergence form inΩ, a bounded open subset of Rn (n ≥ 3).展开更多
This paper deals with a problem proposed by H. Brezis on the existence of positive solutionsto the equation An + u(rt+2)/(n--2) + f(x,u) = 0 under the Neumann boundaly collditionD.u = un/(rt--z), where f(x, u) is a lo...This paper deals with a problem proposed by H. Brezis on the existence of positive solutionsto the equation An + u(rt+2)/(n--2) + f(x,u) = 0 under the Neumann boundaly collditionD.u = un/(rt--z), where f(x, u) is a lower order perturbation of u(n+2)/(n--2) at infinity.展开更多
Using variational method, the authors get an existence result for positive solutions of a superlinear elliptic boundary value problem without assuming the P.S. condition. To prove the results in this paper, the author...Using variational method, the authors get an existence result for positive solutions of a superlinear elliptic boundary value problem without assuming the P.S. condition. To prove the results in this paper, the authors adopt the method of gradient flow and use a new class of truncation functions.展开更多
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the sol...This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.展开更多
In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will...In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal.展开更多
The authors study the regularity of soutions of the GFD-Stokes problem and of some second order linear elliptic partial differential equations related to the PrimitiveEquations of the ocean .The present work generalli...The authors study the regularity of soutions of the GFD-Stokes problem and of some second order linear elliptic partial differential equations related to the PrimitiveEquations of the ocean .The present work generallizes the regularity results in[18] by taking into consideraion the non- homogeneous boundary conditions and teh dependence of solutions on the thickness of the domain occupied by the ocean and its varying bottom topography. These regularity results are important tools in the study of the PEs(see e.g.[6]), and they seem also to possess their own interest.展开更多
This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and th...This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.展开更多
文摘We prove the existence of a positive solution to the problem-Δu=a(x)f(u), x∈Ω, u(x)=0,x∈Ω,where Ω is a bounded domain in R n with smooth boundary, a(x) is allowed to change sign.
文摘Homogenization is concerned with obtaining the average properties of a material. The problem on its own has no easy solution, except in cases like the periodic case, when it can be obtained in closed form. In this paper we consider a numerical solution of the elliptic homogenization problem for the case of rapidly varying tensor or boundary conditions. The method makes use of an adaptive finite element method to correctly capture the rapid change in the tensor or boundary condition. In the numerical experiments we vary the mesh size and do a posteriori error analysis on test problems.
文摘In the paper an inverse boundary value problem for a fourth order elliptic equation with an integral condition of the first kind is investigated. First, the given problem is reduced to an equivalent problem in a certain sense. Then, using the Fourier method the equivalent problem is reduced to solving the system of integral equations. The existence and uniqueness of a solution to the system of integral equation is proved by the contraction mapping principle. This solution is also the unique solution to the equivalent problem. Finally, by equivalence, the theorem of existence and uniqueness of a classical solution to the given problem is proved.
文摘The singularly perturbed problems for the nonlinear elliptic systems in the half space are considered. Under suitable conditions, using the comparison theorem the existence and asymptotic behavior of solution for the boundary value problem are studied.
文摘In this paper, the author studies the regularity of solutions to the Dirichlet problem forequation Lu = f, where L is a second order degenerate elliptic operator in divergence form inΩ, a bounded open subset of Rn (n ≥ 3).
文摘This paper deals with a problem proposed by H. Brezis on the existence of positive solutionsto the equation An + u(rt+2)/(n--2) + f(x,u) = 0 under the Neumann boundaly collditionD.u = un/(rt--z), where f(x, u) is a lower order perturbation of u(n+2)/(n--2) at infinity.
基金Project supported by the National Natural Science Foundation of China and the Research Fund for the Doctoral Program of Higher
文摘Using variational method, the authors get an existence result for positive solutions of a superlinear elliptic boundary value problem without assuming the P.S. condition. To prove the results in this paper, the authors adopt the method of gradient flow and use a new class of truncation functions.
基金supported by the National Natural Science Foundation of China(No.10971019)the GuangxiProvincial Natural Science Foundation of China(No.2010GXNSFA013114)
文摘This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.
基金This research is supported by the Special Funds for Major State Research Projects of China(G 1999032804)
文摘In this paper we consider domain decomposition methods for three-dimensional elliptic problems with Lagrange multipliers, and construct a kind of simple preconditioner for the corresponding interface equation. It will be shown that condition number of the resulting preconditioned interface matrix is almost optimal.
基金This work was partially supported by the National Science Foundation under the grant NSF-DMS 0074334by the Research Fund of Indiana University.
文摘The authors study the regularity of soutions of the GFD-Stokes problem and of some second order linear elliptic partial differential equations related to the PrimitiveEquations of the ocean .The present work generallizes the regularity results in[18] by taking into consideraion the non- homogeneous boundary conditions and teh dependence of solutions on the thickness of the domain occupied by the ocean and its varying bottom topography. These regularity results are important tools in the study of the PEs(see e.g.[6]), and they seem also to possess their own interest.
基金supported by the National Natural Science Foundation of China(No.11171220)the Shanghai Leading Academic Discipline Project(No.XTKX2012)the Hujiang Foundation of China(No.B14005)
文摘This work is devoted to studying a quasilinear elliptic boundary value problem with superlinear nonlinearities in a weighted Sobolev space in a domain of R^N. Based on the Galerkin method, Brouwer's theorem and the weighted compact Sobolev-type embedding theorem, a new result about the existence of solutions is revealed to the problem.
