We investigate positivity sets of nonnegative supersolutions of the fully nonlinear elliptic equations F(x, u,Du,D2u) = 0 in Ω, where Ω is an open subset of RN, and the validity of the strong maximum principle for F(x, u,Du,D2u) = f in Ω, with f ∈ C(Ω) being nonpositive. We obtain geometric characterizations of positivity sets {x ∈ Ω : u(x) > 0} of nonnegative supersolutions u and establish the strong maximum principle under some geometric assumption on the set {x ∈ Ω : f(x) = 0}.

Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle / Birindelli, Isabella; Galise, Giulio; Ishii, Hitoshi. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 374:(2021), pp. 539-564. [10.1090/tran/8226]

Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle

Birindelli, Isabella;Galise, Giulio;
2021

Abstract

We investigate positivity sets of nonnegative supersolutions of the fully nonlinear elliptic equations F(x, u,Du,D2u) = 0 in Ω, where Ω is an open subset of RN, and the validity of the strong maximum principle for F(x, u,Du,D2u) = f in Ω, with f ∈ C(Ω) being nonpositive. We obtain geometric characterizations of positivity sets {x ∈ Ω : u(x) > 0} of nonnegative supersolutions u and establish the strong maximum principle under some geometric assumption on the set {x ∈ Ω : f(x) = 0}.
2021
Fully nonlinear elliptic equations; degenerate elliptic equations; positivity sets; strong maximum principle; truncated Laplacians
01 Pubblicazione su rivista::01a Articolo in rivista
Positivity sets of supersolutions of degenerate elliptic equations and the strong maximum principle / Birindelli, Isabella; Galise, Giulio; Ishii, Hitoshi. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 374:(2021), pp. 539-564. [10.1090/tran/8226]
File allegati a questo prodotto
File Dimensione Formato  
Birindelli_Positivity-sets_2021.pdf

solo gestori archivio

Note: Birindelli-Galise-Ishii
Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Creative commons
Dimensione 353.85 kB
Formato Adobe PDF
353.85 kB Adobe PDF   Contatta l'autore

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/11573/1459872
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact