Related papers: Removable sets for Orlicz-Sobolev spaces

In a complete metric space equipped with a doubling measure and supporting a $(1,1)$-Poincar\'e inequality, we show that every set satisfying a suitable capacitary density condition is removable for Newton-Sobolev functions.

Let $K$ be a compact subset of $\bar{\bold C} ={\bold R}^2$ and let $K^c$ denote its complement. We say $K\in HR$, $K$ is holomorphically removable, if whenever $F:\bar{\bold C} \to\bar{\bold C}$ is a homeomorphism and $F$ is holomorphic…

In this article, we will define the Orlicz space and the Orlicz-Sobolev space, and develop their topological properties. We will also examine their applications to partial differential equations (PDEs), with an emphasis on the use of…

In this article, we investigate the existence of closed vector subspaces (i.e.spaceability) in various nonlinear subsets of Orlicz-Lorentz spaces $\Lambda_{\varphi,w}$, equipped with the Luxemburg norm. If a family of Orlicz functions…

We characterize the removability of H\"older-$\alpha$ graphs with respect to continuous Sobolev $W^{1,2}$ functions. For $\alpha > 2/3$ these graphs are removable, while for $\alpha <2/3$ there exist graphs which are not removable.

We prove the solvability in Sobolev spaces for both divergence and non-divergence form higher order parabolic and elliptic systems in the whole space, on a half space, and on a bounded domain. The leading coefficients are assumed to be…

We obtain sharp embeddings from the Sobolev space $W^{k,2}_0(-1,1)$ into the space $L^1(-1,1)$ and determine the extremal functions. This improves on a previous estimate of the sharp constants of these embeddings due to Kalyabin.

We study removable sets for the Campanato, H\"{o}lder continuous, $L^p_{\text{loc}}$, and Lipschitz functions in Carnot groups. In the former three cases, we characterize removability through the use of capacities with respect to any…

The solvability in Sobolev spaces is proved for divergence form complex-valued higher order parabolic systems in the whole space, on a half space, and on a Reifenberg flat domain. The leading coefficients are assumed to be merely measurable…

We introduce $ \Lambda(\Phi) $-sets as generalizations of $ \Lambda(p) $-sets. These sets are defined in terms of Orlicz norms. We consider $\Lambda(\Phi)$-sets when the Matuszewska-Orlicz index of $ \Phi $ is larger than $ 2 $. When $S$ is…

In this article, the authors establish a new characterization of the Musielak--Orlicz--Sobolev space on $\mathbb{R}^n$, which includes the classical Orlicz--Sobolev space, the weighted Sobolev space and the variable exponent Sobolev space…

We establish the solvability of second order divergence type parabolic systems in Sobolev spaces. The leading coefficients are assumed to be only measurable in one spatial direction on each small parabolic cylinder with the spatial…

An embedding theorem for Sobolev spaces built upon general Musielak-Orlicz norms is offered. These norms are defined in terms of generalized Young functions which also depend on the $x$ variable. Under minimal conditions on the latter…

We present several results on solvability in Sobolev spaces $W^{1}_{p}$ of SPDEs in divergence form in the whole space.

This paper introduces first order Sobolev spaces on certain rectifiable varifolds. These complete locally convex spaces are contained in the generally nonlinear class of generalised weakly differentiable functions and share key functional…

We analyze fine properties of solutions to quasilinear elliptic equations with double phase structure and characterize, in the terms of intrinsic Hausdorff measures, the removable sets for H\"older continuous solutions.

We prove that all Sierpi\'nski spaces in ${\mathbb{S}}^n$, $n\geq 2$, are non-removable for (quasi)conformal maps, generalizing the result of the first named author arXiv:1809.05605. More precisely, we show that for any Sierpi\'nski space…

In this paper, we investigate the extremal structure of the unit ball in the most general classes of Orlicz--Lorentz spaces. the characterizations of extreme points, strongly extreme points, and exposed points are given for Orlicz--Lorentz…

Let $L$ be the divergence form elliptic operator with complex bounded measurable coefficients, $\omega$ the positive concave function on $(0,\infty)$ of strictly critical lower type $p_\oz\in (0, 1]$ and…

We extend several known results on solvability in the Sobolev spaces $W^{1}_{p}$, $p\in[2,\infty)$, of SPDEs in divergence form in $\bR^{d}_{+}$ to equations having coefficients which are discontinuous in the space variable.