Title:
|
Nonexistence results for nonlocal equations with critical and supercritical nonlinearities
|
Author:
|
Ros Oton, Xavier; Serra Montolí, Joaquim
|
Other authors:
|
Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions |
Abstract:
|
We prove nonexistence of nontrivial bounded solutions to some nonlinear problems involving nonlocal operators of the form; [GRAPHICS]; These operators are infinitesimal generators of symmetric Levy processes. Our results apply to even kernels K satisfying that K(y)|y|( n+sigma) is nondecreasing along rays from the origin, for some sigma is an element of (0, 2) in case a ( ij ) equivalent to 0 and for sigma = 2 in case that (a ( ij )) is a positive definite symmetric matrix.; Our nonexistence results concern Dirichlet problems for L in star-shaped domains with critical and supercritical nonlinearities (where the criticality condition is in relation to n and sigma).; We also establish nonexistence of bounded solutions to semilinear equations involving other nonlocal operators such as the higher order fractional Laplacian (- Delta)( s ) (here s > 1) or the fractional p-Laplacian. All these nonexistence results follow from a general variational inequality in the spirit of a classical identity by Pucci and Serrin. |
Abstract:
|
Peer Reviewed |
Subject(s):
|
-35J60 -45K05 -Nonexistence -Integro-differential operators -Supercritical nonlinearities -Fractional Laplacian -FRACTIONAL LAPLACIAN -ELLIPTIC-EQUATIONS -POHOZAEV IDENTITY -OPERATORS -INEQUALITIES -BOUNDARY -35J60 -45K05 |
Rights:
|
|
Document type:
|
Article - Submitted version Article |
Share:
|
|