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BOUNDARY BEHAVIOR OF SUPERHARMONIC FUNCTIONS SATISFYING NONLINEAR INEQUALITIES IN A PLANAR SMOOTH DOMAIN

Part of: Two-dimensional theory Elliptic equations and systems

Published online by Cambridge University Press:  09 October 2009

KENTARO HIRATA
KENTARO HIRATA*
Affiliation:
Faculty of Education and Human Studies, Akita University, Akita 010-8502, Japan (email: hirata@math.akita-u.ac.jp)
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Abstract

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This paper presents a sharp boundary growth estimate for all positive superharmonic functions u in a smooth domain Ω in ℝ2 satisfying the nonlinear inequality where c>0, α∈ℝ and p>0, and δΩ(x) stands for the distance from a point x to the boundary of Ω. A result is applied to show the existence of nontangential limits of such superharmonic functions.

Keywords

superharmonic functionboundary growthnontangential limitnonlinear elliptic equation

MSC classification

Secondary: 31A20: Boundary behavior (theorems of Fatou type, etc.) 35J60: Nonlinear elliptic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 2 , October 2009 , pp. 253 - 261
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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