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Symmetry properties of some solutions to some semilinear elliptic equations

Abstract : In this paper we prove some symmetry results for entire solutions to the semilinear equation -Delta u = f(u), with f nonincreasing in a right neighbourhood of the origin. We consider solutions decaying only in some directions and we give some sufficient conditions for them to be radially symmetric with respect to those variables, such as periodicity or the pointwise decay of some derivatives.
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https://hal-u-picardie.archives-ouvertes.fr/hal-03621422
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Soumis le : lundi 28 mars 2022 - 10:57:11
Dernière modification le : mercredi 14 septembre 2022 - 18:30:29

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  • HAL Id : hal-03621422, version 1

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Alberto Farina, Andrea Malchiodi, Matteo Rizzi. Symmetry properties of some solutions to some semilinear elliptic equations. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2016, 16 (4), pp.1209-1234. ⟨hal-03621422⟩

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