In this paper we prove some results on the boundary behavior of solutions to fractional elliptic problems. Firstly, we establish a Hopf Lemma for solutions to some integro-differential equations. The main novelty of our result is that we do not assume any global condition on the sign of the solutions. Secondly, we show that non-trivial radial solutions cannot have infinitely many zeros accumulating at the boundary. We provide concrete examples to show that the results obtained are sharp.
A fractional Hopf Lemma for sign-changing solutions
Soave, Nicola;
2024-01-01
Abstract
In this paper we prove some results on the boundary behavior of solutions to fractional elliptic problems. Firstly, we establish a Hopf Lemma for solutions to some integro-differential equations. The main novelty of our result is that we do not assume any global condition on the sign of the solutions. Secondly, we show that non-trivial radial solutions cannot have infinitely many zeros accumulating at the boundary. We provide concrete examples to show that the results obtained are sharp.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
DipSoaVal CPDE 2024 arxiv.pdf
Accesso aperto
Tipo di file:
PREPRINT (PRIMA BOZZA)
Dimensione
288.23 kB
Formato
Adobe PDF
|
288.23 kB | Adobe PDF | Visualizza/Apri |
|
DipSoaVal CommPDE 2024.pdf
Accesso riservato
Tipo di file:
PDF EDITORIALE
Dimensione
2.1 MB
Formato
Adobe PDF
|
2.1 MB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
