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- W4376632323 abstract "This article establishes the boundary H{o}lder continuity of stable solutions to semilinear elliptic problems in the optimal range of dimensions $n leq 9$, for $C^{1,1}$ domains. We consider equations $- L u = f(u)$ in a bounded $C^{1,1}$ domain $Omega subset mathbb{R}^n$, with $u = 0$ on $partial Omega$, where $L$ is a linear elliptic operator with variable coefficients and $f in C^1$ is nonnegative, nondecreasing, and convex. The stability of $u$ amounts to the nonnegativity of the principal eigenvalue of the linearized equation $- L - f'(u)$. Our result is new even for the Laplacian, for which [Cabr'{e}, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)] proved the H{o}lder continuity in $C^3$ domains." @default.
- W4376632323 created "2023-05-17" @default.
- W4376632323 creator A5032010588 @default.
- W4376632323 date "2023-05-11" @default.
- W4376632323 modified "2023-10-05" @default.
- W4376632323 title "Boundary H{o}lder continuity of stable solutions to semilinear elliptic problems in $C^{1,1}$ domains" @default.
- W4376632323 doi "https://doi.org/10.48550/arxiv.2305.07062" @default.
- W4376632323 hasPublicationYear "2023" @default.
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