Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 58, Number 4 (2006), 1211-1232.
Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces
We study -harmonic functions in complete metric spaces equipped with a doubling Borel measure supporting a weak -Poincaré inequality, . We establish the barrier classification of regular boundary points from which it also follows that regularity is a local property of the boundary. We also prove boundary regularity at the fixed (given) boundary for solutions of the one-sided obstacle problem on bounded open sets. Regularity is further characterized in several other ways.
Our results apply also to Cheeger -harmonic functions and in the Euclidean setting to -harmonic functions, with the usual assumptions on .
J. Math. Soc. Japan, Volume 58, Number 4 (2006), 1211-1232.
First available in Project Euclid: 21 May 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 31C45: Other generalizations (nonlinear potential theory, etc.) 35B65: Smoothness and regularity of solutions 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 49N60: Regularity of solutions
BJÖRN, Anders; BJÖRN, Jana. Boundary regularity for p-harmonic functions and solutions of the obstacle problem on metric spaces. J. Math. Soc. Japan 58 (2006), no. 4, 1211--1232. doi:10.2969/jmsj/1179759546. https://projecteuclid.org/euclid.jmsj/1179759546