Using the theory of the mixed Hodge structure one can define a notion of exponents of a singularity.In 2000,Hertling proposed a conjecture about the variance of the exponents of a singularity.Here,we prove that the He...Using the theory of the mixed Hodge structure one can define a notion of exponents of a singularity.In 2000,Hertling proposed a conjecture about the variance of the exponents of a singularity.Here,we prove that the Hertling conjecture is true for isolated surface singularities with modality ≤ 2.展开更多
In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequal...In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.展开更多
The main purpose of this paper is to establish the existence of multiple solutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities. It is shown, by means o...The main purpose of this paper is to establish the existence of multiple solutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities. It is shown, by means of variational methods, that under certain conditions, the system has at least two positive solutions.展开更多
In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents -△μ-μ｜x｜^2^-μ=α｜x｜^s^-｜μ｜^2＊（s）-2u＋βα（x）｜u｜^...In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents -△μ-μ｜x｜^2^-μ=α｜x｜^s^-｜μ｜^2＊（s）-2u＋βα（x）｜u｜^r-2u,x∈R^n. By means of the concentration-compactness principle and minimax methods, we obtain infinitely many solutions which tend to zero for suitable positive parameters α,β.展开更多
In this paper, we study the existence result for degenerate elliptic equations with singular potential and critical cone sobolev exponents on singular manifolds. With the help of the variational method and the theory ...In this paper, we study the existence result for degenerate elliptic equations with singular potential and critical cone sobolev exponents on singular manifolds. With the help of the variational method and the theory of genus, we obtain several results under different conditions.展开更多
In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-comp...In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem展开更多
Let B1 С RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical ...Let B1 С RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical Sobolev exponent and singular coefficients：{-div（｜△u｜p-2△u）=｜x｜s｜u｜p＊（s）-2u＋λ｜x｜t｜u｜p-2u, x∈B1, u｜σB1 =0, where t, s〉-p, 2≤p〈N, p＊（s）= （N＋s）pN-p andλ is a real parameter. We show particularly that the above problem exists infinitely many radial solutions if the space dimension N 〉p（p-1）t＋p（p2-p＋1） andλ∈（0,λ1,t）, whereλ1,t is the first eigenvalue of-△p with the Dirichlet boundary condition. Meanwhile, the nonexistence of sign-changing radial solutions is proved if the space dimension N ≤ （ps＋p） min{1, p＋t/p＋s}＋p2p-（p-1） min{1, p＋tp＋s} andλ〉0 is small.展开更多
Based on the theory of variable exponents and BMO norms, we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneous Herz spaces where the two main indices are v...Based on the theory of variable exponents and BMO norms, we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneous Herz spaces where the two main indices are variable exponents.Furthermore, we show that a wide class of commutators generated by BMO functions and sublinear operators satisfy vector-valued inequalities.展开更多
The purpose of this paper is to study a class of elliptic equations with variable exponents. By using the method of regularization and a priori estimates, we obtain the existence of weak solutions to these problems.
In this paper, we introduce Morrey-Herz spaces MKq.p（·）α（·）,λ with variable exponents α（·） and p（·）, and prove the boundedness of multilinear Calderdn-Zygmund singular operators on the ...In this paper, we introduce Morrey-Herz spaces MKq.p（·）α（·）,λ with variable exponents α（·） and p（·）, and prove the boundedness of multilinear Calderdn-Zygmund singular operators on the product of these spaces.展开更多
This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles ...This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent of the system is determined also.展开更多
We prove the boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents.Based on this result,we obtain the boundedness for the multilinear si...We prove the boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents.Based on this result,we obtain the boundedness for the multilinear singular integral operators and two kinds of multilinear singular integral commutators on the above spaces.展开更多
Suppose Ω belong to R^N（N≥3） is a smooth bounded domain,ξi∈Ω,0〈ai〈√μ,μ：=（（N-1）/2）^2,0≤μi〈（√μ-ai）^2,ai〈bi〈ai＋1 and pi：=2N/N-2（1＋ai-bi）are the weighted critical Hardy-Sobolev exponents, i ...Suppose Ω belong to R^N（N≥3） is a smooth bounded domain,ξi∈Ω,0〈ai〈√μ,μ：=（（N-1）/2）^2,0≤μi〈（√μ-ai）^2,ai〈bi〈ai＋1 and pi：=2N/N-2（1＋ai-bi）are the weighted critical Hardy-Sobolev exponents, i = 1, 2,..., k, k ≥ 2. We deal with the conditions that ensure the existence of positive solutions to the multi-singular and multi-critical elliptic problem ∑i=1^k（-div（｜x-ξi｜^-2ai△↓u）-μiu/｜x-ξi｜^2（1＋ai）-u^pi-1/｜x-ξi｜^bipi）=0with Dirichlet boundary condition, which involves the weighted Hardy inequality and the weighted Hardy-Sobolev inequality. The results depend crucially on the parameters ai, bi and #i, i -- 1, 2,..., k.展开更多
Quality control(QC)is an essential procedure in scatterometer wind retrieval,which is used to distinguish good-quality data from poor-quality wind vector cells(WVCs)for the sake of wind applications.The current wind p...Quality control(QC)is an essential procedure in scatterometer wind retrieval,which is used to distinguish good-quality data from poor-quality wind vector cells(WVCs)for the sake of wind applications.The current wind processor of the China-France Oceanography Satellite(CFOSAT)scatterometer(CSCAT)adopts a maximum likelihood estimator(MLE)-based QC method to filter WVCs affected by geophysical noise,such as rainfall and wind variability.As the first Ku-band rotating fan-beam scatterometer,CSCAT can acquire up to 16 observations over a single WVC,giving abundant information with diverse incidence/azimuth angles,as such its MLE statistical characteristics may be different from the previous scatterometers.In this study,several QC indicators,including MLE,its spatially averaged value(MLE_(m)),and the singularity exponents(SE),are analyzed using the collocated Global Precipitation Mission rainfall data as well as buoy data,to compare their sensitivity to rainfall and wind quality.The results show that wind error characteristics of CSCAT under different QC methods are similar to those of other Ku-band scatterometers,i.e.,SE is more suitable than other parameters for the wind QC at outer-swath and nadir regions,while MLE_(m) is the best QC indicator for the sweet region WVCs.Specifically,SE is much more favorable than others at high wind speeds.By combining different indicators,an improved QC method is developed for CSCAT.The validation with the collocated buoy data shows that it accepts more WVCs,and in turn,improves the quality control of CSCAT wind data.展开更多
基金supported by Start-up Fund of Tsinghua University
文摘Using the theory of the mixed Hodge structure one can define a notion of exponents of a singularity.In 2000,Hertling proposed a conjecture about the variance of the exponents of a singularity.Here,we prove that the Hertling conjecture is true for isolated surface singularities with modality ≤ 2.
基金Supported by NSFC(10471047)NSF Guangdong Province(05300159).
文摘In this article, the authors prove the existence and the nonexistence of nontrivial solutions for a semilinear biharmonic equation involving critical exponent by virtue of Mountain Pass Lemma and Sobolev-Hardy inequality.
基金supported by NSFC(10771085)Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Educationthe 985 Program of Jilin University
文摘The main purpose of this paper is to establish the existence of multiple solutions for singular elliptic system involving the critical Sobolev-Hardy exponents and concave-convex nonlinearities. It is shown, by means of variational methods, that under certain conditions, the system has at least two positive solutions.
文摘In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents -△μ-μ｜x｜^2^-μ=α｜x｜^s^-｜μ｜^2＊（s）-2u＋βα（x）｜u｜^r-2u,x∈R^n. By means of the concentration-compactness principle and minimax methods, we obtain infinitely many solutions which tend to zero for suitable positive parameters α,β.
文摘In this paper, we study the existence result for degenerate elliptic equations with singular potential and critical cone sobolev exponents on singular manifolds. With the help of the variational method and the theory of genus, we obtain several results under different conditions.
文摘In this paper, we establish the existence of at least five distinct solutions to a p-Laplacian problems involving critical exponents and singular cylindrical potential, by using the Nehari manifold, concentration-compactness principle and mountain pass theorem
基金supported by the National Natural Science Foundation of China(11326139,11326145)Tian Yuan Foundation(KJLD12067)Hubei Provincial Department of Education(Q20122504)
文摘Let B1 С RN be a unit ball centered at the origin. The main purpose of this paper is to discuss the critical dimension phenomenon for radial solutions of the following quasilinear elliptic problem involving critical Sobolev exponent and singular coefficients：{-div（｜△u｜p-2△u）=｜x｜s｜u｜p＊（s）-2u＋λ｜x｜t｜u｜p-2u, x∈B1, u｜σB1 =0, where t, s〉-p, 2≤p〈N, p＊（s）= （N＋s）pN-p andλ is a real parameter. We show particularly that the above problem exists infinitely many radial solutions if the space dimension N 〉p（p-1）t＋p（p2-p＋1） andλ∈（0,λ1,t）, whereλ1,t is the first eigenvalue of-△p with the Dirichlet boundary condition. Meanwhile, the nonexistence of sign-changing radial solutions is proved if the space dimension N ≤ （ps＋p） min{1, p＋t/p＋s}＋p2p-（p-1） min{1, p＋tp＋s} andλ〉0 is small.
文摘Based on the theory of variable exponents and BMO norms, we prove the vector-valued inequalities for commutators of singular integrals on both homogeneous and inhomogeneous Herz spaces where the two main indices are variable exponents.Furthermore, we show that a wide class of commutators generated by BMO functions and sublinear operators satisfy vector-valued inequalities.
文摘The purpose of this paper is to study a class of elliptic equations with variable exponents. By using the method of regularization and a priori estimates, we obtain the existence of weak solutions to these problems.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271209 and 11371370)NaturalScience Foundation of Nantong University(Grant No.11ZY002)
文摘In this paper, we introduce Morrey-Herz spaces MKq.p（·）α（·）,λ with variable exponents α（·） and p（·）, and prove the boundedness of multilinear Calderdn-Zygmund singular operators on the product of these spaces.
基金supported by the National Natural Science Foundation of China (Grant No. 10771024)
文摘This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent of the system is determined also.
基金supported in part by the National Natural Science Foundationof China(Grant Nos.11926343,11926342,11761026)the Natural Science Foundation of Guangxi Province(Grant No.2020GXNSFAA159085)the Open Project of Anhui University(Grant No.KF2019B02).
文摘We prove the boundedness for a class of multi-sublinear singular integral operators on the product of central Morrey spaces with variable exponents.Based on this result,we obtain the boundedness for the multilinear singular integral operators and two kinds of multilinear singular integral commutators on the above spaces.
基金supported partly by the National Natural Science Foundation of China (10771219)the Science Foundation of the SEAC of China (07ZN03)
文摘Suppose Ω belong to R^N（N≥3） is a smooth bounded domain,ξi∈Ω,0〈ai〈√μ,μ：=（（N-1）/2）^2,0≤μi〈（√μ-ai）^2,ai〈bi〈ai＋1 and pi：=2N/N-2（1＋ai-bi）are the weighted critical Hardy-Sobolev exponents, i = 1, 2,..., k, k ≥ 2. We deal with the conditions that ensure the existence of positive solutions to the multi-singular and multi-critical elliptic problem ∑i=1^k（-div（｜x-ξi｜^-2ai△↓u）-μiu/｜x-ξi｜^2（1＋ai）-u^pi-1/｜x-ξi｜^bipi）=0with Dirichlet boundary condition, which involves the weighted Hardy inequality and the weighted Hardy-Sobolev inequality. The results depend crucially on the parameters ai, bi and #i, i -- 1, 2,..., k.
基金The National Key Research and Development Program of China under contract Nos 2022YFC3104900 and 2022YFC3104902.
文摘Quality control(QC)is an essential procedure in scatterometer wind retrieval,which is used to distinguish good-quality data from poor-quality wind vector cells(WVCs)for the sake of wind applications.The current wind processor of the China-France Oceanography Satellite(CFOSAT)scatterometer(CSCAT)adopts a maximum likelihood estimator(MLE)-based QC method to filter WVCs affected by geophysical noise,such as rainfall and wind variability.As the first Ku-band rotating fan-beam scatterometer,CSCAT can acquire up to 16 observations over a single WVC,giving abundant information with diverse incidence/azimuth angles,as such its MLE statistical characteristics may be different from the previous scatterometers.In this study,several QC indicators,including MLE,its spatially averaged value(MLE_(m)),and the singularity exponents(SE),are analyzed using the collocated Global Precipitation Mission rainfall data as well as buoy data,to compare their sensitivity to rainfall and wind quality.The results show that wind error characteristics of CSCAT under different QC methods are similar to those of other Ku-band scatterometers,i.e.,SE is more suitable than other parameters for the wind QC at outer-swath and nadir regions,while MLE_(m) is the best QC indicator for the sweet region WVCs.Specifically,SE is much more favorable than others at high wind speeds.By combining different indicators,an improved QC method is developed for CSCAT.The validation with the collocated buoy data shows that it accepts more WVCs,and in turn,improves the quality control of CSCAT wind data.
