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http://dx.doi.org/10.4134/CKMS.c160233

UNIQUENESS OF SOLUTIONS FOR THE BOUNDARY VALUE PROBLEM OF CERTAIN NONLINEAR ELLIPTIC OPERATORS VIA p-HARMONIC BOUNDARY

Lee, Yong Hah (Department of Mathematics Education Ewha Womans University)

Publication Information

Communications of the Korean Mathematical Society / v.32, no.4, 2017 , pp. 1025-1031 More about this Journal

Abstract

We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

Keywords

${\mathcal{A}}$ -harmonic function; p-harmonic boundary; boundary value problem;

Citations & Related Records

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