We discuss existence, multiplicity, localisation and stability properties of solutions of the Dirichlet problem associated with the gradient dependent prescribed mean curvature equation in the Lorentz-Minkowski space {−div(∇u/√1−|∇u|²)=f(x,u,∇u) in Ω, u=0 on ∂Ω . The obtained results display various peculiarities, which are due to the special features of the involved differential operator and have no counterpart for elliptic problems driven by other quasilinear differential operators. This research is also motivated by some recent achievements in the study of prescribed mean curvature graphs in certain Friedmann–Lemaître–Robertson–Walker, as well as Schwarzschild–Reissner–Nordström, spacetimes.

The Dirichlet problem for gradient dependent prescribed mean curvature equations in the Lorentz-Minkowski space

CORSATO, CHIARA;OBERSNEL, Franco;OMARI, PIERPAOLO
2017-01-01

Abstract

We discuss existence, multiplicity, localisation and stability properties of solutions of the Dirichlet problem associated with the gradient dependent prescribed mean curvature equation in the Lorentz-Minkowski space {−div(∇u/√1−|∇u|²)=f(x,u,∇u) in Ω, u=0 on ∂Ω . The obtained results display various peculiarities, which are due to the special features of the involved differential operator and have no counterpart for elliptic problems driven by other quasilinear differential operators. This research is also motivated by some recent achievements in the study of prescribed mean curvature graphs in certain Friedmann–Lemaître–Robertson–Walker, as well as Schwarzschild–Reissner–Nordström, spacetimes.
2017
Pubblicato
https://www.degruyter.com/view/j/gmj.2017.24.issue-1/gmj-2016-0078/gmj-2016-0078.xml
File in questo prodotto:
File Dimensione Formato  
COO_LUS16.pdf

accesso aperto

Descrizione: COO_LUS16
Tipologia: Bozza finale post-referaggio (post-print)
Licenza: Digital Rights Management non definito
Dimensione 371.97 kB
Formato Adobe PDF
371.97 kB Adobe PDF Visualizza/Apri
corsato2017.pdf

accesso aperto

Tipologia: Documento in Versione Editoriale
Licenza: Digital Rights Management non definito
Dimensione 662.04 kB
Formato Adobe PDF
662.04 kB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

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: https://hdl.handle.net/11368/2888466
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 13
social impact