Regularity of solutions in semilinear elliptic theory
classification
🧮 math.AP
keywords
equationconditionshskipsemilinearsolutionsbeginbelongconfigurations
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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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