The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boundary 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;
2017

Abstract

The existence of solutions to a class of quasilinear elliptic problems on noncompact Riemannian manifolds, with finite volume, is investigated. Boundary 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.
File in questo prodotto:
File Dimensione Formato  
Barl CM JFA 2017_POST.pdf

accesso aperto

Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 1.39 MB
Formato Adobe PDF
1.39 MB Adobe PDF Visualizza/Apri
Barl CM JFA 2017.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non pubblico (Accesso privato/ristretto)
Dimensione 492.25 kB
Formato Adobe PDF
492.25 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12318/5809
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact