Nonlocal quadratic forms with visibility constraint

Kaßmann M, Wagner V (2018)
arXiv:1810.12289.

Preprint | Englisch
 
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Autor*in
Kaßmann, MoritzUniBi ; Wagner, Vanja
Abstract / Bemerkung
Given a subset $D$ of the Euclidean space, we study nonlocal quadratic forms that take into account tuples $(x,y) \in D \times D$ if and only if the line segment between $x$ and $y$ is contained in $D$. We discuss regularity of the corresponding Dirichlet form leading to the existence of a jump process with visibility constraint. Our main aim is to investigate corresponding Poincar\'{e} inequalities and their scaling properties. For dumbbell shaped domains we show that the forms satisfy a Poincar\'{e} inequality with diffusive scaling. This relates to the rate of convergence of eigenvalues in singularly perturbed domains.
Erscheinungsjahr
2018
Zeitschriftentitel
arXiv:1810.12289
Page URI
https://pub.uni-bielefeld.de/record/2956116

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Kaßmann M, Wagner V. Nonlocal quadratic forms with visibility constraint. arXiv:1810.12289. 2018.
Kaßmann, M., & Wagner, V. (2018). Nonlocal quadratic forms with visibility constraint. arXiv:1810.12289
Kaßmann, M., and Wagner, V. (2018). Nonlocal quadratic forms with visibility constraint. arXiv:1810.12289.
Kaßmann, M., & Wagner, V., 2018. Nonlocal quadratic forms with visibility constraint. arXiv:1810.12289.
M. Kaßmann and V. Wagner, “Nonlocal quadratic forms with visibility constraint”, arXiv:1810.12289, 2018.
Kaßmann, M., Wagner, V.: Nonlocal quadratic forms with visibility constraint. arXiv:1810.12289. (2018).
Kaßmann, Moritz, and Wagner, Vanja. “Nonlocal quadratic forms with visibility constraint”. arXiv:1810.12289 (2018).

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