WELL-POSEDNESS OF DISCONTINUOUS BOUNDARY-VALUE PROBLEMS FOR NONLINEAR ELLIPTIC COMPLEX EQUATIONS IN MULTIPLY CONNECTED DOMAINS | |
Wen, Guo-Chun | |
2013 | |
关键词 | Well-posedness discontinuous boundary value problem nonlinear elliptic complex equation A priori estimate existence of solutions |
英文摘要 | In the first part of this article, we study a discontinuous Riemann-Hilbert problem for nonlinear uniformly elliptic complex equations of first order in multiply connected domains. First we show its well-posedness. Then we give the representation of solutions for a modified Riemann-Hilbert problem for the complex equations. Then we obtain a priori estimates of the solutions and verify the solvability of the modified problem by using the Leray-Schauder theorem. Then the solvability of the original discontinuous Riemann-Hilbert boundary-value problem is obtained. In the second part, we study a discontinuous Poincare boundary-value problem for nonlinear elliptic equations of second order in multiply connected domains. First we formulate the boundary-value problem and show its new well-posedness. Next we obtain the representation of solutions and obtain a priori estimates for the solutions of a modified Poincare problem. Then with estimates and the method of parameter extension, we obtain the solvability of the discontinuous Poincare problem.; Mathematics, Applied; Mathematics; SCI(E); 0; ARTICLE |
语种 | 英语 |
出处 | SCI |
出版者 | electronic journal of differential equations |
内容类型 | 其他 |
源URL | [http://hdl.handle.net/20.500.11897/314322] ![]() |
专题 | 数学科学学院 |
推荐引用方式 GB/T 7714 | Wen, Guo-Chun. WELL-POSEDNESS OF DISCONTINUOUS BOUNDARY-VALUE PROBLEMS FOR NONLINEAR ELLIPTIC COMPLEX EQUATIONS IN MULTIPLY CONNECTED DOMAINS. 2013-01-01. |
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