This article studies the Dirichlet eigenvalue problem for the Laplacian equations △u = -λu, x ∈Ω , u = 0, x ∈δΩ, where Ω belong to R^n is a smooth bounded convex domain. By using the method of appropriate barr...This article studies the Dirichlet eigenvalue problem for the Laplacian equations △u = -λu, x ∈Ω , u = 0, x ∈δΩ, where Ω belong to R^n is a smooth bounded convex domain. By using the method of appropriate barrier function combined with the maximum principle, authors obtain a sharp lower bound of the difference of the first two eigenvalues for the Dirichlet eigenvalue problem. This study improves the result of S.T. Yau et al.展开更多
This paper is devoted lo the study of regularity of solutions for Dirichlet probelm ofnonlinear degenerate elliptic equations in two dimensional case. A sufficient condition fortheir solutions in C<sup>3+α</...This paper is devoted lo the study of regularity of solutions for Dirichlet probelm ofnonlinear degenerate elliptic equations in two dimensional case. A sufficient condition fortheir solutions in C<sup>3+α</sup>（Ω） to be certainly in C<sup>∞</sup>（Ω） is given.展开更多
The existence of C~∞ -solutions to Dirichlet problem for Monge-Ampere equation degenerate on boundary is proved, and some applications to the equation prescribed Gaussian curvature are also given.
基金This research was supported by the National Natural Science Foundation of Chinathe Scientific Research Foundation of the Ministry of Education of China (02JA790014)+1 种基金the Natural Science Foundation of Fujian Province Education Department(JB00078)the Developmental Foundation of Science and Technology of Fuzhou University (2004-XQ-16)
文摘This article studies the Dirichlet eigenvalue problem for the Laplacian equations △u = -λu, x ∈Ω , u = 0, x ∈δΩ, where Ω belong to R^n is a smooth bounded convex domain. By using the method of appropriate barrier function combined with the maximum principle, authors obtain a sharp lower bound of the difference of the first two eigenvalues for the Dirichlet eigenvalue problem. This study improves the result of S.T. Yau et al.
文摘This paper is devoted lo the study of regularity of solutions for Dirichlet probelm ofnonlinear degenerate elliptic equations in two dimensional case. A sufficient condition fortheir solutions in C<sup>3+α</sup>（Ω） to be certainly in C<sup>∞</sup>（Ω） is given.
基金The project supported by the National Natural Science Foundation.
文摘The existence of C~∞ -solutions to Dirichlet problem for Monge-Ampere equation degenerate on boundary is proved, and some applications to the equation prescribed Gaussian curvature are also given.
