The ∂ˉ-Robin Laplacian

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 s...

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Detalhes bibliográficos
Autor: Duran, Joaquim
Formato: artículo
Fecha de publicación:2026
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/489178
Acesso em linha:http://hdl.handle.net/2072/489178
Access Level:acceso abierto
Palavra-chave:Spectral theory
Resolvent convergence
Eigenvalues
51
Descrição
Resumo: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.