dc.contributor.author
Erneta, I.U.
dc.date.accessioned
2023-08-29T11:06:39Z
dc.date.accessioned
2024-09-19T14:35:34Z
dc.date.available
2023-08-29T11:06:39Z
dc.date.available
2024-09-19T14:35:34Z
dc.date.issued
2023-02-01
dc.identifier.uri
http://hdl.handle.net/2072/536864
dc.description.abstract
In this paper we extend the interior regularity results for stable solutions in [Cabré, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)] to operators with variable coefficients. We show that stable solutions to the semilinear elliptic equation aij(x)uij+bi(x)ui+f(u) = 0 are Hölder continuous in the optimal range of dimensions n ≤ 9. Our bounds are independent of the nonlinearity f ∈ C1, which we assume to be nonnegative. The main achievement of our work is to make the constants in our estimates depend on the C1 norm of aij and the C0 norm of bi, instead of their C2 and C1 norms, respectively, which arise in a first approach to the computations. © 2023 American Institute of Mathematical Sciences. All rights reserved.
eng
dc.description.sponsorship
Acknowledgements. The author acknowledges financial support from MINECO through the María de Maeztu Program (MDM-2014-0445-18-1). He is additionally supported by grants MTM2017-84214-C2-1-P and RED2018-102650-T funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. The author thanks Xavier Cabréfor his patient guidance and useful discussions on the topic of this article.
dc.format.extent
45 p.
cat
dc.publisher
American Institute of Mathematical Sciences
cat
dc.relation.ispartof
Communications on Pure and Applied Analysis
cat
dc.rights
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dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
A priori estimates; interior regularity; operators with coefficients; semilinear equations; Stable solutions
cat
dc.title
STABLE SOLUTIONS TO SEMILINEAR ELLIPTIC EQUATIONS FOR OPERATORS WITH VARIABLE COEFFICIENTS
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/submittedVersion
cat
dc.identifier.doi
10.3934/cpaa.2022162
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
