Nondiffusive variational problems with distributional and weak gradient constraints
| Autor: | Antil Harbir, Arndt Rafael, Rautenberg Carlos N., Verma Deepanshu |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Advances in Nonlinear Analysis, Vol 11, Iss 1, Pp 1466-1495 (2022) |
| Druh dokumentu: | article |
| ISSN: | 2191-950X 2022-0227 |
| DOI: | 10.1515/anona-2022-0227 |
| Popis: | In this article, we consider nondiffusive variational problems with mixed boundary conditions and (distributional and weak) gradient constraints. The upper bound in the constraint is either a function or a Borel measure, leading to the state space being a Sobolev one or the space of functions of bounded variation. We address existence and uniqueness of the model under low regularity assumptions, and rigorously identify its Fenchel pre-dual problem. The latter in some cases is posed on a nonstandard space of Borel measures with square integrable divergences. We also establish existence and uniqueness of solution to this pre-dual problem under some assumptions. We conclude the article by introducing a mixed finite-element method to solve the primal-dual system. The numerical examples illustrate the theoretical findings. |
| Databáze: | Directory of Open Access Journals |
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