Related papers: Sobolev homeomorphic extensions

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 give a quantitative characterization of traces on the boundary of Sobolev maps in $\dot{W}^{1,p}(\mathcal M, \mathcal N)$, where $\mathcal{M}$ and $\mathcal{N}$ are compact Riemannian manifolds, $\partial \mathcal{M} \neq \emptyset$: the…

We discuss the space of complex exponential maps $\Ek\colon z\mapsto e^{z}+\kappa$. We prove that every hyperbolic component $W$ has connected boundary, and there is a conformal isomorphism $\Phi_W\colon W\to\half^-$ which extends to a…

We show that the number of noncommensurable lattices, hence also that of maximal lattices in SO(1,n) is at least exponential. To do so we construct large families of noncommensurable hybrid hyperbolic (Gromov/Piatetski-Shapiro) manifolds.

In complex dynamics, the boundaries of higher dimensional hyperbolic components in holomorphic families of polynomials or rational maps are mysterious objects, whose topological and analytic properties are fundamental problems. In this…

We provide a complete characterization of those self-homeomorphisms of the unit circle that admit homeomorphic extensions to the unit disk belonging to bi--Orlicz--Sobolev spaces. Our results generalize classical criteria from the Sobolev…

Let $\Omega,\Omega'\subset\mathbb{R}^3$ be Lipschitz domains, let $f_m:\Omega\to\Omega'$ be a sequence of homeomorphisms with prescribed Dirichlet boundary condition and $\sup_m \int_{\Omega}(|Df_m|^2+1/J^2_{f_m})<\infty$. Let $f$ be a weak…

We construct a solution operator for $\overline{\partial}$ equation that gains $\frac{1}{2}$ derivative in the fractional Sobolev space $H^{s,p}$ on bounded strictly pseudoconvex domains in $\mathbb{C}^n$ with $C^2$ boundary, for all $1 < p…

In this paper, we consider Hartree-type equations on the two-dimensional torus and on the plane. We prove polynomial bounds on the growth of high Sobolev norms of solutions to these equations. The proofs of our results are based on the…

The tensorization problem for Sobolev spaces asks for a characterization of how the Sobolev space on a product metric measure space $X\times Y$ can be determined from its factors. We show that two natural descriptions of the Sobolev space…

There are known trace and extension theorems relating functions in a weighted Sobolev space in a domain U to functions in a Besov space on the boundary bU. We extend these theorems to the case where the Sobolev exponent p is less than one…

Let $L^{m,p}(\R^n)$ denote the Sobolev space of functions whose $m$-th derivatives lie in $L^p(\R^n)$, and assume that $p>n$. For $E \subset \R^n$, denote by $L^{m,p}(E)$ the space of restrictions to $E$ of functions $F \in L^{m,p}(\R^n)$.…

First of all, we establish compactness of continuous mappings of the Orlicz--Sobolev classes $W^{1,\varphi}_{\rm loc}$ with the Calderon type condition on $\varphi$ and, in particular, of the Sobolev classes $W^{1,p}_{\rm loc}$ for $p>n-1$…

We consider asymptotically hyperbolic manifolds whose metrics have Sobolev-class regularity, and introduce several technical tools for studying PDEs on such manifolds. Our results employ two novel families of function spaces suitable for…

For some class of mappings, there are investigated problems connected with a possibility of continuous extension to a boundary on Riemannian manifolds. In particular, for so-called ring mappings, there is proved a result related to…

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 construct homotopy formulas for the $\overline\partial$-equation on convex domains of finite type that have optimal Sobolev and H\"older estimates. For a bounded smooth finite type convex domain $\Omega\subset\mathbb C^n$ that has…

We derive estimates in a weighted Sobolev space $W^{k,p}_{\mu}(D)$ for a homotopy operator on a bounded strictly pseudoconvex domain $D$ of $C^2$ boundary in ${\C}^n$. As a result, we show that given any $2n < p < \infty$, $k > 1$, $q \geq…

This paper studies the relations between extendability of different classes of Sobolev $W^{1,1}$ and $BV$ functions from closed sets in general metric measure spaces. Under the assumption that the metric measure space satisfies a weak…

We prove the solvability in Sobolev spaces $W^{1,2}_p$, $p>d+1$, of the terminal-boundary value problem for a class of fully nonlinear parabolic equations, including parabolic Bellman's equations, in bounded cylindrical domains with VMO…