Dokážeme, že ve dvou dimenzích je inverze homeomorfismu s konečnou variací také zobrazení s konečnou variací. Ve více dimenzích dokážeme, že $f^{-1}$ má konečnou variaci, pokud $f\in W^{1,1}(\Omega;\rn)$ je homeomorfismus a $|Df|$ leží v Lorentzově prostoru $L^{n-1,1}(\Omega)$. (cs)
We show that the inverse of a planar homeomorphism of bounded variation is also of bounded variation. In higher dimensions we show that $f^{-1}$ is of bounded variation provided that $f\in W^{1,1}(\Omega;\rn)$ is a homeomorphism with $|Df|$ in the Lorentz space $L^{n-1,1}(\Omega)$.
We show that the inverse of a planar homeomorphism of bounded variation is also of bounded variation. In higher dimensions we show that $f^{-1}$ is of bounded variation provided that $f\in W^{1,1}(\Omega;\rn)$ is a homeomorphism with $|Df|$ in the Lorentz space $L^{n-1,1}(\Omega)$. (en)