Regularity of solutions in semilinear elliptic theory

preprint2016arXivOpen access

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.

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Regularity of solutions in semilinear elliptic theory

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