Non-diffusive Variational Problems with Distributional and Weak Gradient Constraints

06/23/2021 ∙ by Harbir Antil, et al. ∙ 0

In this paper, we consider non-diffusive 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 non-standard space of Borel measures with square integrable divergences. We also establish existence and uniqueness of solutions to this pre-dual problem under some assumptions. We conclude the paper by introducing a mixed finite-element method to solve the primal-dual system. The numerical examples confirm our theoretical findings.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 24

page 25

page 26

page 27

page 28

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.