Related papers: Trace theory for Sobolev mappings into a manifold

We define a tracelike transformation to be a natural family of conjugation invariant maps $T_{x,C}: hom_C(x,x) \to hom_C(1,1)$ for all dualisable objects $x$ in any symmetric monoidal infinity-category $C$. This generalises the trace from…

We study notions of homotopy in the Newtonian space $N^{1,p}(X;Y)$ of Sobolev type maps between metric spaces. After studying the properties and relations of two different notions we prove a compactness result for sequences in homotopy…

For every symmetrically normed ideal $\mathcal{E}$ of compact operators, we give a criterion for the existence of a continuous singular trace on $\mathcal{E}$. We also give a criterion for the existence of a continuous singular trace on…

We introduce the manifold of {\it restricted} $n\times n$ positive semidefinite matrices of fixed rank $p$, denoted $S(n,p)^{*}$. The manifold itself is an open and dense submanifold of $S(n,p)$, the manifold of $n\times n$ positive…

We study traces of elements of fractional Sobolev spaces $H_p^\alpha(\mathbb{R}^n)$ on closed subsets $\Gamma$ of $\mathbb{R}^n$, given as the supports of suitable measures $\mu$. We prove that if these measures satisfy localized upper…

This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often…

We show that, under certain regularity assumptions, there exists a linear extension operator.

A slight extension of a construction due to Calabi-Rosenlicht (and later Gabard, Baillif and others) produces a typically non-metrizable $n$-manifold $\mathbb{P}$ by gluing two copies of the open upper half-space $\mathbb{H}_{++}$ in…

Given a function $f : A \to \mathbb{R}^n$ of a certain regularity defined on some open subset $A \subseteq \mathbb{R}^m$, it is a classical problem of analysis to investigate whether the function can be extended to all of $\mathbb{R}^m$ in…

Let $\mathbb X$ and $\mathbb Y$ be $\ell$-connected Jordan domains, $\ell \in \mathbb N$, with rectifiable boundaries in the complex plane. We prove that any boundary homeomorphism $\varphi \colon \partial \mathbb X \to \partial \mathbb Y$…

We present weighted Sobolev spaces and prove a trace theorem for the spaces. As an application, we discuss non-zero boundary value problems for parabolic equations. The weighted parabolic Sobolev spaces we consider are designed, in…

We study the interpolation property of Sobolev spaces of order 1 denoted by $W^{1}_{p,V}$, arising from Schr\"{o}dinger operators with positive potential. We show that for $1\leq p_1<p<p_2<q_{0}$ with $p>s_0$, $W^{1}_{p,V}$ is a real…

Let $\mathcal{M}$ be a semifinite von Neumann algebra equipped with a normal faithful semifinite trace $\tau$, and let $L_p(\mathcal{M})$ denote the associated noncommutative $L_p$-space for $1<p<\infty$. Let $n\in\mathbb{N}$ and let $a, b$…

Let $p$ be an odd prime, and fix integers $m$ and $n$ such that $0<m<n\leq (p-1)(p-2)$. We give a $p$-local homotopy decomposition for the loop space of the complex Stiefel manifold $W_{n,m}$. Similar decompositions are given for the loop…

We define a trace map for every cohomological correspondence in the motivic stable homotopy category over a general base scheme, which takes values in the twisted bivariant groups. Local contributions to the trace map give rise to quadratic…

We are going to show that on bounded Lipschitz domain $D$: both $C_{c}^{\infty}(D)$, the set of smooth functions on $D$ with compact support, and $C_{0}^{\infty}(D)$, the set of smooth functions on $D$ with (extension) zero boundary, are…

We study the Sobolev trace constant for functions defined in a bounded domain $\O$ that vanish in the subset $A.$ We find a formula for the first variation of the Sobolev trace with respect to hole. As a consequence of this formula, we…

In this paper, we establish the existence of a bounded, linear extension operator $T: L^{2,p}(E) \to L^{2,p}(\mathbb{R}^2)$ when $1<p<2$ and $E$ is a finite subset of $\mathbb{R}^2$ contained in a line.

Let $L^{m,p}(\mathbb{R}^n)$ be the homogeneous Sobolev space for $p \in (n,\infty)$, $\mu$ be a Borel regular measure on $\mathbb{R}^n$, and $L^{m,p}(\mathbb{R}^n) + L^p(d\mu)$ be the space of Borel measurable functions with finite seminorm…

The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of locally Sobolev functions on domains in the Euclidean space.…