Lower semicontinuity, Stoilow factorization and principal maps
Analysis of PDEs
2025-09-16 v3 Complex Variables
Abstract
We consider a strengthening of the usual quasiconvexity condition of Morrey in two dimensions, which allows us to prove lower semicontinuity for functionals which are unbounded as the determinant vanishes. This notion, that we call principal quasiconvexity, arose from the planar theory of quasiconformal mappings and mappings of finite distortion. We compare it with other quasiconvexity conditions that have appeared in the literature and provide a number of concrete examples of principally quasiconvex functionals that are not polyconvex. The Stoilow factorization, that in the context of maps of integrable distortion was developed by Iwaniec and \v{S}ver\'ak, plays a prominent role in our approach.
Cite
@article{arxiv.2401.16138,
title = {Lower semicontinuity, Stoilow factorization and principal maps},
author = {Kari Astala and Daniel Faraco and André Guerra and Aleksis Koski and Jan Kristensen},
journal= {arXiv preprint arXiv:2401.16138},
year = {2025}
}
Comments
34 pages