Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models

Elvise Berchio; Alberto Ferrero; Maria Vallarino

doi:10.1007/s00030-015-0318-1

Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models

Elvise Berchio, Alberto Ferrero, Maria Vallarino

Dipartimento di Scienze e Innovazione Tecnologica

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

We consider least energy solutions to the nonlinear equation -Δ_gu=f(r,u) posed on a class of Riemannian models (M,g) of dimension n≥2 which include the classical hyperbolic space Hⁿ as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is proved for quite general nonlinearities f(r, u), where r denotes the geodesic distance from the pole of M.

Lingua originale	Inglese
pagine (da-a)	1167-1193
Numero di pagine	27
Rivista	Nonlinear Differential Equations and Applications
Volume	22
Numero di pubblicazione	5
DOI	https://doi.org/10.1007/s00030-015-0318-1
Stato di pubblicazione	Pubblicato - 26 ott 2015

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abstract = "We consider least energy solutions to the nonlinear equation -Δgu=f(r,u) posed on a class of Riemannian models (M,g) of dimension n≥2 which include the classical hyperbolic space Hn as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is proved for quite general nonlinearities f(r, u), where r denotes the geodesic distance from the pole of M.",

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AB - We consider least energy solutions to the nonlinear equation -Δgu=f(r,u) posed on a class of Riemannian models (M,g) of dimension n≥2 which include the classical hyperbolic space Hn as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is proved for quite general nonlinearities f(r, u), where r denotes the geodesic distance from the pole of M.

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Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models

Abstract

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