Regularity of solutions in semilinear elliptic theory

Abstract

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

References in corpus (2)

• Cross-shaped and Degenerate Singularities in an Unstable Elliptic Free Boundary Problem
• Partial analyticity and nodal sets for nonlinear elliptic systems