We investigate the existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the nonexistence regimes. For the existence results, we make use of a particular class of weighted Sobolev spaces to compensate for boundary singularities which are naturally built in the problem.
Abatangelo N., Cozzi M. (2021). An elliptic boundary value problem with fractional nonlinearity. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 53(3), 3577-3601 [10.1137/20M1342641].
An elliptic boundary value problem with fractional nonlinearity
Abatangelo N.;
2021
Abstract
We investigate the existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the nonexistence regimes. For the existence results, we make use of a particular class of weighted Sobolev spaces to compensate for boundary singularities which are naturally built in the problem.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
20m1342641.pdf
accesso aperto
Tipo:
Versione (PDF) editoriale
Licenza:
Licenza per accesso libero gratuito
Dimensione
427.02 kB
Formato
Adobe PDF
|
427.02 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
