LMAM, School of Mathematical Sciences
Peking University
Beijing 100871, China
email: Wengc@math.pku.edu.cn
Guo-Chun Wen
Abstract:
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.
Submitted November 1, 2013. Published November 15, 2013.
Math Subject Classifications: 35J56, 35J25, 35J60, 35B45.
Key Words: Well-posedness; discontinuous boundary value problem;
nonlinear elliptic complex equation; A priori estimate;
existence of solutions.
Show me the PDF file (330 KB), TEX file, and other files for this article.
|
Guo-Chun Wen LMAM, School of Mathematical Sciences Peking University Beijing 100871, China email: Wengc@math.pku.edu.cn |
|---|
Return to the EJDE web page