Jacobians of Sobolev and BV homeomorphisms and their limits

Abstract

In the class of homeomorphisms, we are studying the correspondence of the topological orientation (i.e. sense-preserving or sense-reversing) and the analyt- ical orientation (i.e. the sign of Jacobian). In R3 , in was previously known for W1,p homeomorphisms and their weak limits. In our thesis, we prove this cor- respondence for BV homeomorphisms and their weak-* limits in R3 . Moreover, we also give the results for W2,p homeomorphisms in any dimension. 1

V této práci zkoumáme souvislost mezi topologickým pojmem orientace a znaménkem Jakobiánu ve třídě homeomorfismů. V R3 byla tato souvislost známa pro W1,p homeomorfismy a jejich slabé limity. My výsledek rozšiřujeme na BV homeomorfismy a jejich slabé-* limity v R3 . Navíc uvádíme výsledky i pro W2,p homeomorfismy v libovolné dimenzi. 1