Journal
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Volume 33, Issue 3, Pages 699-717Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036141000372179
Keywords
p-Laplacian; viscosity solutions; p-superharmonic functions
Categories
Ask authors/readers for more resources
We discuss and compare various notions of weak solution for the p-Laplace equation -div(\delu\(p-2)delu) = 0 and its parabolic counterpart u(t) - div(\delu\(p-2)delu) = 0. In addition to the usual Sobolev weak solutions based on integration by parts, we consider the p-superharmonic (or p-superparabolic) functions from nonlinear potential theory and the viscosity solutions based on generalized pointwise derivatives ( jets). Our main result states that in both the elliptic and the parabolic case, the viscosity supersolutions coincide with the potential-theoretic supersolutions.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available