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arXiv · 1601.05219

Regularity of solutions in semilinear elliptic theory

Emanuel Indrei·Andreas Minne·Levon Nurbekyan
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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 $f$ 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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Emanuel Indrei, Andreas Minne, Levon Nurbekyan. 2016-01-20. Regularity of solutions in semilinear elliptic theory. https://arxiv.org/abs/1601.05219

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