This is the second part of the paper for the mathematical study of nonconforming rotated Q1 element (NRQ1 hereafter) on arbitrary quadrilateral meshes. Some Poincare Inequalities are proved without assuming the quasi-...This is the second part of the paper for the mathematical study of nonconforming rotated Q1 element (NRQ1 hereafter) on arbitrary quadrilateral meshes. Some Poincare Inequalities are proved without assuming the quasi-uniformity of the mesh subdivision. A discrete trace inequality is also proved.展开更多
In this paper, we consider a class of superlinear elliptic problems involving trac- tional Laplacian （-△）s/2u = λf（u） in a bounded smooth domain with zero Diriehlet bound- ary condition. We use the method on har...In this paper, we consider a class of superlinear elliptic problems involving trac- tional Laplacian （-△）s/2u = λf（u） in a bounded smooth domain with zero Diriehlet bound- ary condition. We use the method on harmonic extension to study the dependence of the number of sign-changing solutions on the parameter λ.展开更多
In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type.An explicit L2 norm estimate for the gradient of the solution of this problem is est...In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type.An explicit L2 norm estimate for the gradient of the solution of this problem is established.This leads to an explicit bound of the H1 norm of this solution.Note that the obtained upper-bound is not optimal.展开更多
基金The work of P.-B.Ming was partially supported by the National Natural Science Foundation of China 10201033
文摘This is the second part of the paper for the mathematical study of nonconforming rotated Q1 element (NRQ1 hereafter) on arbitrary quadrilateral meshes. Some Poincare Inequalities are proved without assuming the quasi-uniformity of the mesh subdivision. A discrete trace inequality is also proved.
基金supported by China Postdoctoral Science Foundation Funded Project(2016M592088)National Natural Science Foundation of China-NSAF(11271305)
文摘In this paper, we consider a class of superlinear elliptic problems involving trac- tional Laplacian （-△）s/2u = λf（u） in a bounded smooth domain with zero Diriehlet bound- ary condition. We use the method on harmonic extension to study the dependence of the number of sign-changing solutions on the parameter λ.
文摘In this paper we consider the Lamé system on a polygonal convex domain with mixed boundary conditions of Dirichlet-Neumann type.An explicit L2 norm estimate for the gradient of the solution of this problem is established.This leads to an explicit bound of the H1 norm of this solution.Note that the obtained upper-bound is not optimal.
