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General Boundary Value Problems for Nonlinear Uniformly Elliptic Equations in Multiply Connected Infinite Domains
School of Mathematical Sciences, Peking University, Beijing, China
Mathematic Department, Beijing Technology and Business University, Beijing, China
Uniformed Services University of the Health Sciences, Bethesda, USA
- 1 School of Mathematical Sciences, Peking University, Beijing, China
- 2 Mathematic Department, Beijing Technology and Business University, Beijing, China
- 3 Uniformed Services University of the Health Sciences, Bethesda, USA
International Journal of Modern Nonlinear Theory and Application·Volume 02 (2013)·Pages 170–175·Published 19 August 2013·DOI10.4236/ijmnta.2013.23024
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Abstract
This article discusses the general boundary value problem for the nonlinear uniformly elliptic equation of second order in D (0.1) and the boundary condition ,(0.2) in a multiply connected infinite domain D with the boundary T. The above boundary value problem is called Problem G. Problem G extends the work [8] in which the equation (0.1) includes a nonlinear lower term and the boundary condition (0.2) is more general. If the complex equation (0.1) and the boundary condition (0.2) meet certain assumptions, some solvability results for Problem G can be obtained. By using reduction to absurdity, we first discuss a priori estimates of solutions and solvability for a modified problem. Then we present results on solvability of Problem G.
KeywordsBoundary Value ProblemsNonlinear Elliptic EquationsMultiply Connected Infinite Domains
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