Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schr\
By Fritz Gesztesy, M. Mitrea. 2008
104 citations recorded by the source corpus.
We study generalized Robin boundary conditions, Robin-to-Dirichlet maps, and Krein-type resolvent formulas for Schr\"odinger operators on bounded Lipschitz domains in $\bbR^n$, $n\ge 2$. We also discuss the case of bounded $C^{1,r}$-domains, $(1/2)
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a38c4b0013bb8f084749cf6f172aa3ec34586aa5
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Robin-to-Robin Maps and Krein-Type Resolvent Formulas for Schr\ (2008, background): “Finally, a notational comment: For obvious reasons in connection with quantum mechanical applications, we will, with a slight abuse of notation, dub −∆ (rather than ∆) as the “Laplacian” in this paper.”
- Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalities (2008, background): “Schr¨odinger operators on bounded Lipschitz domains with nonlocal Robin boundary conditions of the form (1.1), have been very recently discussed in great detail in [23] an d [24], and our treatment of nonlocal Robin Laplacians in this paper naturally builds upon these two papers.”
- Hodge decompositions with mixed boundary conditions and applications to partial differential equations on lipschitz manifolds (2011, methodology): “Here, we have largely followed the presentation in [ 34 , 35].”
- Elliptic operators, Dirichlet-to-Neumann maps and quasi boundary triples (2012, unknown): “…see, e.g. [Derkach and Malamud, 1991; Gesztesy, Makarov and Tsekanovskii, 1998; Krĕın, 1946; Langer and Textorius, 1977; Pankrashkin, 2006; Saakjan, 1965] for the general case and, e.g. [Gesztesy and Mitrea, 2008, 2009, 2011; Grubb, 2008; Posilicano and Raimondi, 2009] for applications to PDEs.”
- A description of all self-adjoint extensions of the Laplacian and Kreĭn-type resolvent formulas on non-smooth domains (2009, methodology): “ension Φ of φ, and that eγN is a bounded extension of the Neumann trace operator γN defined in (3.9). Corresponding to the endpoint cases s= 0,1 of (3.11), the following result has been established in [56]: Lemma 3.2. Assume Hypothesis 2.1. Then the Neumann trace operator (3.9) also extends to eγN : ”