English

Regularity of solutions in semilinear elliptic theory

Analysis of PDEs 2016-01-21 v1

Abstract

We study the semilinear Poisson equation \begin{equation} \label{pro} \Delta u = f(x, u) \hskip .2 in \text{in} \hskip .2 in B_1. \end{equation} Our main results provide conditions on ff which ensure that weak solutions of this equation belong to C1,1(B1/2)C^{1,1}(B_{1/2}). In some configurations, the conditions are sharp.

Keywords

Cite

@article{arxiv.1601.05219,
  title  = {Regularity of solutions in semilinear elliptic theory},
  author = {Emanuel Indrei and Andreas Minne and Levon Nurbekyan},
  journal= {arXiv preprint arXiv:1601.05219},
  year   = {2016}
}