Nondiffusive variational problems with distributional and weak gradient constraints Article Swipe
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· 2022
· Open Access
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· DOI: https://doi.org/10.1515/anona-2022-0227
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.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1515/anona-2022-0227
- OA Status
- gold
- Cited By
- 5
- References
- 34
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3174620509