Lower semicontinuity, Stoilow factorization and principal maps
arxiv(2024)
摘要
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 Šverák, plays a
prominent role in our approach.
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