Nonlocal quadratic forms with visibility constraint

Kaßmann M, Wagner V (2022)
Mathematische Zeitschrift .

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | 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) is an element of D x 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 Poincare inequalities and their scaling properties. For dumbbell shaped domains we show that the forms satisfy a Poincare inequality with diffusive scaling. This relates to the rate of convergence of eigenvalues in singularly perturbed domains.
Stichworte
Function spaces; Nonlocal Dirichlet forms; Poincare inequalities; Integro-differential operators; Jump processes
Erscheinungsjahr
2022
Zeitschriftentitel
Mathematische Zeitschrift
ISSN
0025-5874
eISSN
1432-1823
Page URI
https://pub.uni-bielefeld.de/record/2962207

Zitieren

Kaßmann M, Wagner V. Nonlocal quadratic forms with visibility constraint. Mathematische Zeitschrift . 2022.
Kaßmann, M., & Wagner, V. (2022). Nonlocal quadratic forms with visibility constraint. Mathematische Zeitschrift . https://doi.org/10.1007/s00209-022-03004-9
Kaßmann, M., and Wagner, V. (2022). Nonlocal quadratic forms with visibility constraint. Mathematische Zeitschrift .
Kaßmann, M., & Wagner, V., 2022. Nonlocal quadratic forms with visibility constraint. Mathematische Zeitschrift .
M. Kaßmann and V. Wagner, “Nonlocal quadratic forms with visibility constraint”, Mathematische Zeitschrift , 2022.
Kaßmann, M., Wagner, V.: Nonlocal quadratic forms with visibility constraint. Mathematische Zeitschrift . (2022).
Kaßmann, Moritz, and Wagner, Vanja. “Nonlocal quadratic forms with visibility constraint”. Mathematische Zeitschrift (2022).

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arXiv: 1810.12289

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