A Spherical Harnack Inequality for Singular Solutions of Nonlinear Elliptic Equations
Journal
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Journal Volume
30
Journal Issue
44624
Pages
713-738
Date Issued
2001
Author(s)
Chen C.-C
Lin C.-S.
Abstract
We consider a positive singular solution of where g(t) is locally bounded and positive for t > 0, r is a closed subset of B1 with vanishing Newton capacity, BR is the open ball of radius R and center 0 in R", and n > 3. By employing the method of moving planes and the localization method of R. Schoen, we prove the following inequality, where c is a positive constant and d (x) is the distance from x to r, provided that is nonincreasing in t for t large. This inequality is new even when u (x) is radially symmetric. © 2001 Scuola Normale Superiore. All rights reserved.
Type
journal article