English

The Lavrentiev phenomenon in calculus of variations with differential forms

Analysis of PDEs 2023-05-09 v1

Abstract

In this article we study convex non-autonomous variational problems with differential forms and corresponding function spaces. We introduce a general framework for constructing counterexamples to the Lavrentiev gap, which we apply to several models, including the double phase, borderline case of double phase potential, and variable exponent. The results for the borderline case of double phase potential provide new insights even for the scalar case, i.e., variational problems with 00-forms.

Keywords

Cite

@article{arxiv.2305.04726,
  title  = {The Lavrentiev phenomenon in calculus of variations with differential forms},
  author = {Anna Kh. Balci and Mikhail Surnachev},
  journal= {arXiv preprint arXiv:2305.04726},
  year   = {2023}
}