Nondiffusive variational problems with distributional and weak gradient constraints Article Swipe

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Harbir Antil , Rafael Arndt , Carlos N. Rautenberg , Deepanshu Verma ·

YOU? · · 2022 · Open Access · · 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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Mathematics Uniqueness Square-integrable function Bounded function Sobolev space Constraint (computer-aided design) Mathematical analysis Boundary (topology) Applied mathematics Variational inequality Space (punctuation) Function space Borel measure Bounded variation Function (biology) Probability measure Geometry Philosophy Biology Evolutionary biology Linguistics

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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
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DOI: https://doi.org/10.1515/anona-2022-0227

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Title: Nondiffusive variational problems with distributional and weak gradient constraints

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Language: en

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Publication year: 2022

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Publication date: 2022-01-01

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Authors: Harbir Antil, Rafael Arndt, Carlos N. Rautenberg, Deepanshu Verma

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Landing page: https://doi.org/10.1515/anona-2022-0227

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Concepts: Mathematics, Uniqueness, Square-integrable function, Bounded function, Sobolev space, Constraint (computer-aided design), Mathematical analysis, Boundary (topology), Applied mathematics, Variational inequality, Space (punctuation), Function space, Borel measure, Bounded variation, Function (biology), Probability measure, Geometry, Philosophy, Biology, Evolutionary biology, Linguistics

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Cited by: 5

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