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- W4320167592 abstract "We study stable solutions to fractional semilinear equations $(-Delta)^s u = f(u)$ in $Omega subset mathbb{R}^n$, for convex nonlinearities $f$, and under the Dirichlet exterior condition $u=g$ in $mathbb{R}^n setminus Omega$ with general $g$. We establish a uniqueness and a classification result, and we show that weak (energy) stable solutions can be approximated by a sequence of bounded (and hence regular) stable solutions to similar problems. As an application of our results, we establish the interior regularity of weak (energy) stable solutions to the problem for the half-Laplacian in dimensions $1 leq n leq 4$." @default.
- W4320167592 created "2023-02-13" @default.
- W4320167592 creator A5004763893 @default.
- W4320167592 date "2022-10-05" @default.
- W4320167592 modified "2023-09-29" @default.
- W4320167592 title "Stable solutions to fractional semilinear equations: uniqueness, classification, and approximation results" @default.
- W4320167592 doi "https://doi.org/10.48550/arxiv.2210.02477" @default.
- W4320167592 hasPublicationYear "2022" @default.
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