Nonlocal quadratic forms with visibility constraint

@article{Kassmann2022NonlocalQF,
  title={Nonlocal quadratic forms with visibility constraint},
  author={Moritz Kassmann and Vanja Wagner},
  journal={Mathematische Zeitschrift},
  year={2022},
  volume={301},
  pages={3087 - 3107}
}
Given a subset D of the Euclidean space, we study nonlocal quadratic forms that take into account tuples (x,y)∈D×D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(x,y) \in D \times D$$\end{document} if and only if the line segment between x and y is contained in D. We discuss regularity of the corresponding… 

Fractional Sobolev spaces with power weights

We investigate the form of the closure of the smooth, compactly supported functions C∞ c (Ω) in the weighted fractional Sobolev space W (Ω) for bounded Ω. We focus on the weights w, v being powers of

Reduction of integration domain in Triebel–Lizorkin spaces

We investigate the comparability of generalized Triebel-Lizorkin and Sobolev seminorms on uniform and non-uniform sets when the integration domain is truncated according to the distance from the

References

SHOWING 1-10 OF 25 REFERENCES

A note on the trace theorem for Besov-type spaces of generalized smoothness on d-sets

The main goal of this paper is to give a complete proof of the trace theorem for Besov-type spaces of generalized smoothness associated with complete Bernstein functions satisfying certain scaling

A T(1) Theorem for Fractional Sobolev Spaces on Domains

Given any uniform domain $$\Omega $$Ω, the Triebel–Lizorkin space $$F^s_{p,q}(\Omega )$$Fp,qs(Ω) with $$0<s<1$$0<s<1 and $$1<p,q<\infty $$1<p,q<∞ can be equipped with a norm in terms of first-order

Eigenvalues and Resonances for Domains with Tubes: Neumann Boundary Conditions

Abstract We consider unbounded regions which consist of a bounded domain C joined to an unbounded region E by a tube T(ϵ) whose cross-section is of small diameter ϵ. On such a region, we consider the

Reduction of integration domain in Triebel–Lizorkin spaces

We investigate the comparability of generalized Triebel-Lizorkin and Sobolev seminorms on uniform and non-uniform sets when the integration domain is truncated according to the distance from the

Function Spaces and Potential Theory

The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge

Lévy Processes

Lévy processes are random processes on Euclidean space that are stochastically continuous and have stationary independent increments. They, and their stochastic integrals, have become useful tools in

Sobolev Inequalities in Familiar and Unfamiliar Settings

The classical Sobolev inequalities play a key role in analysis in Euclidean spaces and in the study of solutions of partial differential equations. In fact, they are extremely flexible tools and are

On comparability of integral forms