We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem.
A Brezis-Nirenberg type result for mixed local and nonlocal operators
Biagi, Stefano;
2025-01-01
Abstract
We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding Sobolev inequality, detecting the optimal constant, which we show that is never achieved. Moreover, we present an existence (and nonexistence) theory for the corresponding subcritical perturbation problem.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
S. Biagi, S. Dipierro, E. Valdinoci, E. Vecchi - A Brezis-Nirenberg type result for mixed local and nonlocal operators.pdf
Accesso riservato
Dimensione
525.47 kB
Formato
Adobe PDF
|
525.47 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
