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arXiv · 2303.05310

The boundedness of stable solutions to semilinear elliptic equations with linear lower bound on nonlinearities

Fa Peng
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Abstract

Let $2\le n\le9$. Suppose that $f:R\to R$ is locally Lipschitz function satisfying $f(t)\ge A\min\{0,t\}-K$ for all $t\in R$ with some constant $A\ge0$ and $K\ge 0$. We establish an a priori interior Hölder regularity of $C^2$-stable solution to the semilinear elliptic equation $-Δu=f(u)$. If, in addition, $f$ is nondecreasing and convex, we obtain the interior Hölder regularity of $W^{1,2}$-stable solutions. Note that the dimension $n\le9$ is optimal.

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Fa Peng. 2023-07-11. The boundedness of stable solutions to semilinear elliptic equations with linear lower bound on nonlinearities. https://arxiv.org/abs/2303.05310

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