| Autor: |
Antil, Harbir, Arndt, Rafael, Rautenberg, Carlos N., Verma, Deepanshu |
| Zdroj: |
Advances in Nonlinear Analysis; November 2021, Vol. 11 Issue: 1 p1466-1495, 30p |
| Abstrakt: |
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: |
Supplemental Index |
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