General Boundary Value Problems for Nonlinear Uniformly Elliptic Equations in Multiply Connected Infinite Domains

Guochun Wen, Yanhui Zhang, Dechang Chen

Mathematic Department, Beijing Technology and Business University, Beijing, China.
School of Mathematical Sciences, Peking University, Beijing, China.
Uniformed Services University of the Health Sciences, Bethesda, USA.

DOI: 10.4236/ijmnta.2013.23024                

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.

Keywords

Boundary Value Problems; Nonlinear Elliptic Equations; Multiply Connected Infinite Domains

Conflicts of Interest

The authors declare no conflicts of interest.

References

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