Aim of this paper is to give a regularity result for weak solutions of a fractional Laplacian equation. In order to get this result we first prove a maximum principle and then, using it, an interior and boundary regularity result for weak solutions of the problem. As a consequence of our regularity result, along the paper we also deduce that the first eigenfunction of the fractional Laplacian is strictly positive.
Weak and viscosity solutions of the fractional Laplace equation
SERVADEI, RAFFAELLA;
2014
Abstract
Aim of this paper is to give a regularity result for weak solutions of a fractional Laplacian equation. In order to get this result we first prove a maximum principle and then, using it, an interior and boundary regularity result for weak solutions of the problem. As a consequence of our regularity result, along the paper we also deduce that the first eigenfunction of the fractional Laplacian is strictly positive.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
