Naslov
Nonlocal quadratic forms with visibility constraint

Autori
Kassmann, Moritz ; Wagner, Vanja

Izvornik
Mathematische Zeitschrift (0025-5874) 301 (2022), 3; 3087-3107

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Function spaces ; Nonlocal Dirichlet forms ; Poincaré inequalities ; Integro-differential operators ; Jump processes

Sažetak
Given a subset D of the Euclidean space, we study nonlocal quadratic forms that take into account tuples (x, y) ∈ D × 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 Poincaré inequalities and their scaling properties. For dumbbell shaped domains we show that the forms satisfy a Poincaré inequality with diffusive scaling. This relates to the rate of convergence of eigenvalues in singularly perturbed domains.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA