Maximum principles, sliding techniques and applications to nonlocal equations
Date
2007-05-10
Authors
Coville, Jerome
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
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[u] := J ⋆ u - u is also obtained. The proofs of the uniqueness and monotonicity essentially rely on the sliding method and the strong maximum principle.
Description
Keywords
Nonlocal diffusion operators, Maximum principles, Sliding methods
Citation
Coville, J. (2007). Maximum principles, sliding techniques and applications to nonlocal equations. <i>Electronic Journal of Differential Equations, 2007</i>(68), pp. 1-23.
Rights
Attribution 4.0 International