In this paper, we consider semilinear elliptic problems in a bounded domain Ω contained in a given unbounded Lipschitz domain C⊂ RN . Our aim is to study how the energy of a solution behaves with respect to volume-preserving variations of the domain Ω inside C . Once a rigorous variational approach to this question is set, we focus on the cases when C is a cone or a cylinder and we consider spherical sectors and radial solutions or bounded cylinders and special one-dimensional solutions, respectively. In these cases, we show both stability and instability results, which have connections with related overdetermined problems.
Energy Stability for a Class of Semilinear Elliptic Problems
Iacopetti A.;
2024-01-01
Abstract
In this paper, we consider semilinear elliptic problems in a bounded domain Ω contained in a given unbounded Lipschitz domain C⊂ RN . Our aim is to study how the energy of a solution behaves with respect to volume-preserving variations of the domain Ω inside C . Once a rigorous variational approach to this question is set, we focus on the cases when C is a cone or a cylinder and we consider spherical sectors and radial solutions or bounded cylinders and special one-dimensional solutions, respectively. In these cases, we show both stability and instability results, which have connections with related overdetermined problems.File | Dimensione | Formato | |
---|---|---|---|
Energy_stability_postprint.pdf
Accesso aperto
Descrizione: Versione post-print
Tipo di file:
POSTPRINT (VERSIONE FINALE DELL’AUTORE)
Dimensione
563.02 kB
Formato
Adobe PDF
|
563.02 kB | Adobe PDF | Visualizza/Apri |
s12220-023-01525-1.pdf
Accesso aperto
Descrizione: licenza CC BY 4.0
Tipo di file:
PDF EDITORIALE
Dimensione
618.12 kB
Formato
Adobe PDF
|
618.12 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.