Related papers: On Trace Theorems for Sobolev Spaces

We consider hilbert spaces of holomorphic functions in Cartan domains (in particular in ball and polydisk) and operator of restriction of holomorphic function to a submanifold in Shilov boundary. We discuss conditions when this operator…

In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all…

In this paper, we discuss Bernoulli's principle to the 3-dimensional incompressible Euler equation in a bounded local Lipschitz domain $\Omega\subset\mathbb{R}^{3}$ with a Lipschitz boundary. Using topological properties of the level set…

We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains $O \subset R^d$ with both theoretical and numerical purpose. We use N.V. Krylov's framework of…

In this article, for an optimal range of the smoothness parameter $s$ that depends (quantitatively) on the geometric makeup of the underlying space, the authors identify purely measure theoretic conditions that fully characterize embedding…

We prove a monotone Sobolev extension theorem for maps to Jordan domains with rectifiable boundary in metric surfaces of locally finite Hausdorff 2-measure. This is then used to prove a uniformization result for compact metric surfaces by…

We introduce intrinsic Sobolev-Slobodeckij spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak H\"ormander condition. We prove continuous embeddings into Lorentz and intrinsic H\"older spaces. We also prove…

Given a connected Riemannian manifold $\mathcal{N}$, an \(m\)--dimensional Riemannian manifold $\mathcal{M}$ which is either compact or the Euclidean space, $p\in [1, +\infty)$ and $s\in (0,1]$, we establish, for the problems of…

We consider the question of whether a domain with uniformly thick boundary at all locations and at all scales has a large portion of its boundary visible from the interior; here, "visibility" indicates the existence of John curves…

We develop various quantitative estimates for the anisotropic Maxwell system in Lipschitz domains, with a focus on how the estimates precisely depend on the Lipschitz character of the domain. We pay special attention to trace operators and…

In this paper, we consider the space $\mathrm{BV}^{\mathbb A}(\Omega)$ of functions of bounded $\mathbb A$-variation. For a given first order linear homogeneous differential operator with constant coefficients $\mathbb A$, this is the space…

We construct and investigate the properties of tempered ultradistribution spaces in Sobolev spaces. A new Sobolev space preserving the original properties and condition whose derivatives are linear continuous operators embedding in $L^p$…

We study the homeomorphic extension of biholomorphisms between convex domains in $\mathbb C^d$ without boundary regularity and boundedness assumptions. Our approach relies on methods from coarse geometry, namely the correspondence between…

Given any uniform domain $\Omega$, the Triebel-Lizorkin space $F^s_{p,q}(\Omega)$ with $0<s<1$ and $1<p,q<\infty$ can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to…

We define the chain Sobolev space on a possibly non-complete metric measure space in terms of chain upper gradients. In this context, $\varepsilon$-chains are a finite collection of points with distance at most $\varepsilon$ between…

We study compactness and boundedness of embeddings from Sobolev type spaces on metric spaces into $L^q$ spaces with respect to another measure. The considered Sobolev spaces can be of fractional order and some statements allow also…

In this note we prove a trace theorem in fractional spaces with variable exponents. To be more precise, we show that if $p\colon\overline{\Omega}\times \overline{\Omega}\to (1,\infty)$ and $q:\partial \Omega \rightarrow (1,\infty)$ are…

We apply Selberg's trace formula to solve problems in hyperbolic band theory, a recently developed extension of Bloch theory to model band structures on experimentally realized hyperbolic lattices. For this purpose we incorporate the…

We develop a sharp boundary trace theory in arbitrary bounded Lipschitz domains which, in contrast to classical results, allows "forbidden" endpoints and permits the consideration of functions exhibiting very limited regularity. This is…

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…