UNIQUENESS OF SOLUTIONS FOR THE BOUNDARY VALUE PROBLEM OF CERTAIN NONLINEAR ELLIPTIC OPERATORS VIA p-HARMONIC BOUNDARY
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초록
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 $f$.
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 $f$.
참고문헌 (6)
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