On divergent fractional Laplace equations
Analysis of PDEs
2021-02-04 v2
Abstract
We consider the divergent fractional Laplace operator presented in [Dipierro-Savin-Valdinoci, Rev. Mat. Iberoam.] and we prove three types of results. Firstly, we show that any given function can be locally shadowed by a solution of a divergent fractional Laplace equation which is also prescribed in a neighborhood of infinity. Secondly, we take into account the Dirichlet problem for the divergent fractional Laplace equation, proving the existence of a solution and characterizing its multiplicity. Finally, we take into account the case of nonlinear equations, obtaining a new approximation results. These results maintain their interest also in the case of functions for which the fractional Laplacian can be defined in the usual sense.
Cite
@article{arxiv.1907.11376,
title = {On divergent fractional Laplace equations},
author = {Serena Dipierro and Ovidiu Savin and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1907.11376},
year = {2021}
}