On global absence of Lavrentiev gap for functionals with (p,q)-growth
Analysis of PDEs
2023-06-02 v3
Abstract
This pre-print has now been superseded by arXiv:2305.19934 and will not be published. We prove that for convex vectorial functionals with (p,q)-growth the Lavrentiev phenomenon does not occur up to the boundary when (p,q) are suitably restricted. Under minimal assumptions on the regularity of the domain and the boundary data, we obtain results for autonomous and non-autonomous functionals, under natural, controlled and controlled duality growth bounds.
Keywords
Cite
@article{arxiv.2210.15454,
title = {On global absence of Lavrentiev gap for functionals with (p,q)-growth},
author = {Lukas Koch},
journal= {arXiv preprint arXiv:2210.15454},
year = {2023}
}
Comments
This pre-print has been superseded by arXiv:2305.19934. v3. Corrected the proof of Lemma 7, this requires stronger assumptions on the domain