Maximum principles, sliding techniques and applications to nonlocal equations
| dc.contributor.author | Coville, Jerome | |
| dc.date.accessioned | 2021-08-06T19:38:37Z | |
| dc.date.available | 2021-08-06T19:38:37Z | |
| dc.date.issued | 2007-05-10 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 23 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/14230 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2007, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Nonlocal diffusion operators | |
| dc.subject | Maximum principles | |
| dc.subject | Sliding methods | |
| dc.title | Maximum principles, sliding techniques and applications to nonlocal equations | |
| dc.type | Article |