tailieunhanh - báo cáo hóa học:" Research Article The Boundary Value Problem of the Equations with Nonnegative Characteristic Form"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article The Boundary Value Problem of the Equations with Nonnegative Characteristic Form | Hindawi Publishing Corporation Boundary Value Problems Volume 2010 Article ID 208085 23 pages doi 2010 208085 Research Article The Boundary Value Problem of the Equations with Nonnegative Characteristic Form Limei Li and Tian Ma Mathematical College Sichuan University Chengdu 610064 China Correspondence should be addressed to Limei Li matlilm@ and Tian Ma matian56@ Received 22 May 2010 Accepted 7 July 2010 Academic Editor Claudianor Alves Copyright 2010 L. Li and T. Ma. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We study the generalized Keldys-Fichera boundary value problem for a class of higher order equations with nonnegative characteristic. By using the acute angle principle and the Holder inequalities and Young inequalities we discuss the existence of the weak solution. Then by using the inverse Holder inequalities we obtain the regularity of the weak solution in the anisotropic Sobolev space. 1. Introduction Keldys 1 studies the boundary problem for linear elliptic equations with degenerationg on the boundary. For the linear elliptic equations with nonnegative characteristic forms Oleinik and Radkevich 2 had discussed the Keldys-Fichera boundary value problem. In 1989 Ma and Yu 3 studied the existence of weak solution for the Keldys-Fichera boundary value of the nonlinear degenerate elliptic equations of second-order. Chen 4 and Chen and Xuan 5 Li 6 and Wang 7 had investigated the existence and the regularity of degenerate elliptic equations by using different methods. In this paper we study the generalized Keldys-Fichera boundary value problem which is a kind of new boundary conditions for a class of higher-order equations with nonnegative characteristic form. We discuss the existence and uniqueness of weak solution by using the acute angle principle then study the .