The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boudary value problems, with homogeneous Neumann conditions, in possibly irregular Euclidean domains are included as a special instance. A nontrivial solution is shown to exist under an unconventional growth condition on the right-hand side, which depends on the geometry of the underlying manifold. The identification of the critical growth is a crucial step in our analysis, and entails the use of the isocapacitary function of the manifold. A condition involving its isoperimetric function is also provided.

Quasilinear elliptic equations on noncompact Riemannian manifolds / Barletta, Giuseppina; Cianchi, Andrea; Maz'Ya, Vladimir. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - STAMPA. - 273:(2017), pp. 3426-3462. [10.1016/j.jfa.2017.08.018]

Quasilinear elliptic equations on noncompact Riemannian manifolds

CIANCHI, ANDREA;
2017

Abstract

The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boudary value problems, with homogeneous Neumann conditions, in possibly irregular Euclidean domains are included as a special instance. A nontrivial solution is shown to exist under an unconventional growth condition on the right-hand side, which depends on the geometry of the underlying manifold. The identification of the critical growth is a crucial step in our analysis, and entails the use of the isocapacitary function of the manifold. A condition involving its isoperimetric function is also provided.
2017
273
3426
3462
Barletta, Giuseppina; Cianchi, Andrea; Maz'Ya, Vladimir
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1101758
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