Skip to Main content Skip to Navigation
Journal articles

Maximum principles, sliding techniques and applications to nonlocal equations

Abstract : This paper is devoted to the study of maximum principles holding for some nonlocal diffusion operators defined in (half-) bounded domains and its applications to obtain qualitative behaviors of solutions of some nonlinear problems. It is shown that, as in the classical case, the nonlocal diffusion considered satisfies a weak and a strong maximum principle. Uniqueness and monotonicity of solutions of nonlinear equations are therefore expected as in the classical case. It is first presented a simple proof of this qualitative behavior and the weak/strong maximum principle. An optimal condition to have a strong maximum for operator M := J star u - u is also obtained. The proofs of the uniqueness and monotonicity essentially rely on the sliding method and the strong maximum principle
Complete list of metadata

Cited literature [40 references]  Display  Hide  Download

https://hal.inrae.fr/hal-02654682
Contributor : Migration Prodinra <>
Submitted on : Friday, May 29, 2020 - 9:45:46 PM
Last modification on : Tuesday, August 18, 2020 - 3:34:03 PM

File

2007-EJDE-Coville_1.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Jerome Coville. Maximum principles, sliding techniques and applications to nonlocal equations. Electronic Journal of Differential Equations, Texas State University, Department of Mathematics, 2007, 2007 (68), 23 p. ⟨hal-02654682⟩

Share

Metrics

Record views

15

Files downloads

68