Alexander Egorov (Sobolev Institute of Mathematics)
Stability of classes of mappings and quasiconvex functions
Abstract.
We consider classes of solutions $u:U\to\mathbb{R}^m$
to partial differential relations $F(u'(x))=G(u'(x))$
a.e.\ in $U\subset\mathbb{R}^n$ with
quasiconvex functions $F:\mathbb{R}^{m\times n}\to\mathbb{R}$ and
null Lagrangians $G:\mathbb{R}^{m\times n}\to\mathbb{R}$.
We study stability problems for these classes.
The theorems presented in the talk generalize
some well-known results on stability of classes of holomorphic functions,
conformal transformations, and homotheties.
The case when $F$ is convex was considered in {Egor2003}.
References
{Egor2003}
Egorov,~A.~A. Stability of Classes of Solutions to Partial Differential
Relations Constructed by Convex and Quasiaffine Functions. (Russian).
Proceedings on geometry and analysis.
International conference-school dedicated to the memory of
A.~D.~Alexandrov (1912--1999),
Novosibirsk, Russia, September 9--20, 2002.
Novosibirsk: Izdatel'stvo Instituta Matematiki. 275--288 (2003).
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