Boundedness of stable solutions to semilinear elliptic equations: a survey
Analysis of PDEs
2017-04-21 v1
Abstract
This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known estimates that hold for all nonlinearities. Such estimates are known to hold up to dimension 4. They are expected to be true also in dimensions 5 to 9, but this is still an open problem which has only been established in the radial case.
Keywords
Cite
@article{arxiv.1704.06063,
title = {Boundedness of stable solutions to semilinear elliptic equations: a survey},
author = {Xavier Cabre},
journal= {arXiv preprint arXiv:1704.06063},
year = {2017}
}