Regularity of the inverse of a Sobolev homeomorphism in space

Abstract

Let Ω ⊂ Rn be open. Given a homeomorphism of finite distortion with |Df| in the Lorentz space Ln−1, 1 (Ω), we show that and f−1 has finite distortion. A class of counterexamples demonstrating sharpness of the results is constructed.

Bi-Sobolev mappings and elliptic equations in the plane

“…We know that f −1 ∈ W 1,1 loc is a mapping of finite distortion (see [14] or [8]) and that f is differentiable almost everywhere [23]. Therefore we can use (2.3) for f −1 and (2.1) to obtain…”

Sharpness of the differentiability almost everywhere and capacitary estimates for Sobolev mappings

“…To prove Theorem 1.3 we need to find a way to map Cantor set onto another Cantor set by a homeomorphism. We will do this by using so-called canonical parametrizations and canonical transformations which were first introduced by Hencl, Koskela and Malý in [5].…”

О Регулярности Отображений, Обратных К Соболевским

“…Другими методами теорема 4 доказана в [56] при n = 2, q = 1, p = 2, ∞. Кроме того, при n > 2, q = n − 1, p = n усилена теорема 4.1 из [58].…”