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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