dc.contributor.author
Duran, Joaquim
dc.date.accessioned
2026-01-22T08:28:58Z
dc.date.available
2026-01-22T08:28:58Z
dc.date.issued
2026-06-01
dc.identifier.uri
http://hdl.handle.net/2072/489178
dc.description.abstract
We study the family of operators {ℛ_a}_(a∈[0,+∞))associated to the Robin-type problems in a bounded domain Ω⊂R^2
{︄−Δu=f in Ω,
2ν¯∂_(z¯)u+au=0 on ∂Ω,
and their dependency on the boundary parameter a as it moves along [0,+∞). In this regard, we study the convergence of such operators in a resolvent sense. We also describe the eigenvalues of such operators and show some of their properties, both for all fifixed aand as functions of the parameter a. As shall be seen in more detail in the paper [23], the eigenvalues of these operators characterize the positive eigenvalues of quantum dot Dirac operators.
ca
dc.description.sponsorship
The author is supported by the Spanish grants PID2021-123903NB-I00 and RED2022-134784-T funded by MCIN/AEI/10.13039/501100011033, by ERDF A way of making Europe”, and by the Catalan grant 2021-SGR-00087. This work is supported by the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M), and more specifically by the grant CEX2020-001084-M-20-1. The author acknowledges CERCA Programme/Generalitat de Catalunya for institutional support.
ca
dc.format.extent
54 p.
ca
dc.relation.ispartof
Journal of Mathematical Analysis and Applications
ca
dc.rights
© 2026 The Author(s)
ca
dc.rights
Attribution 4.0 International
*
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
*
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Spectral theory
ca
dc.subject.other
Resolvent convergence
ca
dc.subject.other
Eigenvalues
ca
dc.title
The ∂ˉ-Robin Laplacian
ca
dc.type
info:eu-repo/semantics/article
ca
dc.description.version
info:eu-repo/semantics/publishedVersion
ca
dc.identifier.doi
10.1016/j.jmaa.2026.130411
ca
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
