Related papers: Sobolev homeomorphic extensions onto John domains

Let $\Omega \subset \mathbb{R}^n$ be a domain that supports the $p$-Poincar\'e inequality. Given a homeomorphism $\varphi \in L^1_p(\Omega)$, for $p>n$ we show the domain $\varphi(\Omega)$ has finite geodesic diameter. This result has a…

We introduce a prime end-type theory on complete Kobayashi hyperbolic manifolds using horosphere sequences. This allows to introduce a new notion of boundary-new even in the unit disc in the complex space-the horosphere boundary, and a…

We consider conformal homeomorphisms $\varphi$ of generalized Jordan domains $U$ onto planar domains $\Omega$ %, possibly {\bf infinitely connected}, that satisfy both of the next two conditions: (1) at most countably many boundary…

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques…

In this paper we prove a new version of the Schoenflies extension theorem for collared domains in Euclidean n-space: for 1 < p < n, locally bi-Lipschitz homeomorphisms between collared domains with locally p-integrable, second-order weak…

We have proved that homeomorphisms of domains of Euclidean space, inverse of which distort the modulus of families of curves by Poletskii type, have a continuous extension to isolated boundary point.

We give a full characterization of circle homeomorphisms which admit a homeomorphic extension to the unit disk with finite bi-Sobolev norm. As a special case, a bi-conformal variant of the famous Beurling-Ahlfors extension theorem is…

We characterize bounded simply-connected planar $W^{1,p}$-extension domains for $1 < p <2$ as those bounded domains $\Omega \subset \mathbb R^2$ for which any two points $z_1,z_2 \in \mathbb R^2 \setminus \Omega$ can be connected with a…

Motivated by manifold-constrained homogenization problems, we construct suitable extensions for Sobolev functions defined on a perforated domain and taking values in a compact, connected $C^2$-manifold without boundary. The proof combines a…

Let $X, Y \subset \mathbb{R}^n$ be Lipschitz domains, and suppose there is a homeomorphism $\varphi \colon \overline{X} \to \overline{Y}$. We consider the class of Sobolev mappings $f \in W^{1,n} (X, \mathbb{R}^n)$ with a strictly positive…

We prove that almost every level set of a Sobolev function in a planar domain consists of points, Jordan curves, or homeomorphic copies of an interval. For monotone Sobolev functions in the plane we have the stronger conclusion that almost…

We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to the closures of the domains. Our conditions involve the…

For a simply connected domain $G$, let $\partial_{a}G$ be the set of accessible points in $\partial G$ and let $\partial_{n} G=\partial G-\partial_{a}G$. A point $a\in\partial G$ is called semi-unreachable if there is a crosscut $J$ of $G$…

Let $\alpha$ \in (0; 1). We show that any $\alpha$-H\"older homeomorphism from the unit circle in the plane to the plane can be extended to an $\alpha$-H\"{o}lder homeomorphism from the whole unit disc.

It is given a canonical representation of prime ends in regular spatial domains and, on this basis, it is studied the boundary behavior of the so-called lower Q-homeomorphisms that are the natural generalization of the quasiconformal…

We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to…

We investigate the set of uniform limits of polynomials on any closed Jordan domain with respect to the chordal metric $\chi$ on $\mathbb{C}\cup\{\infty \}$. We conclude that Mergelyan's Theorem may be extended to the case of uniform…

We give direct proofs and constructions of the trace and extension theorems for Sobolev mappings in $W^{1, 1} (M, N)$, where $M$ is Riemannian manifold with compact boundary $\partial M$ and $N$ is a complete Riemannian manifold. The…

Given a bounded n-connected domain in the plane bounded by non-intersecting Jordan curves, and given one point on each boundary curve, L. Bieberbach proved that there exists a proper holomorphic mapping of the domain onto the unit disc that…

Trace classes of Sobolev-type functions in metric spaces are subject of this paper. In particular, functions on domains whose boundary has an upper codimension-$\theta$ bound are considered. Based on a Poincar\'e inequality, existence of a…