Linear theory for a mixed operator with Neumann conditions
Analysis of PDEs
2020-06-09 v1
Abstract
We consider here a new type of mixed local and nonlocal equation under suitable Neumann conditions. We discuss the spectral properties associated to a weighted eigenvalue problem and present a global bound for subsolutions. The Neumann condition that we take into account comprises, as a particular case, the one that has been recently introduced in [S. Dipierro, X. Ros-Oton, E. Valdinoci, Rev. Mat. Iberoam. (2017)]. Also, the results that we present here find a natural application to a logistic equation motivated by biological problems that has been recently considered in [S. Dipierro, E. Proietti Lippi, E. Valdinoci, preprint (2020)].
Cite
@article{arxiv.2006.03850,
title = {Linear theory for a mixed operator with Neumann conditions},
author = {Serena Dipierro and Edoardo Proietti Lippi and Enrico Valdinoci},
journal= {arXiv preprint arXiv:2006.03850},
year = {2020}
}