The Dirichlet-to-Neumann operator on rough domains
By Wolfgang Arendt, A. T. Elst. 2010
101 citations recorded by the source corpus.
Abstract We consider a bounded connected open set Ω ⊂ R d whose boundary Γ has a finite ( d − 1 ) -dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operator D 0 on L 2 ( Γ ) by form methods. The operator − D 0 is self-adjoint and generates a contractive C 0 -semigroup S = ( S t ) t > 0 on L 2 ( Γ ) . We show that the asymptotic behaviour of S t as t → ∞ is related to properties of the trace of functions in H 1 ( Ω ) which Ω may or may not have.
Subfields: Computational Theory and Mathematics, Mathematical Physics, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/ab2cf7879760f903129845323156d3c664c6a170
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In Computational Theory and Mathematics
- Wolfgang Arendt
- S. Hassi
- H. D. de Snoo
- Daniel Daners
- Jussi Behrndt
- Rafe Mazzeo
- Mahamadi Warma
- Dorin Bucur
In Mathematical Physics
- Jussi Behrndt
- H. D. de Snoo
- S. Hassi
- Daniel Daners
- Wolfgang Arendt
- Rafe Mazzeo
- Carlos Lizama
- V. Keyantuo
In Numerical Analysis
Citations in the corpus
- Non-positivity of the semigroup generated by the Dirichlet-to-Neumann operator (2014, background): “A rigorous treatment of this approach on non-smooth domains can be found in [2,4,5].”
- Boundary Value Problems, Weyl Functions, and Differential Operators (2020, background): “Furthermore, the recent contributions [35, 36, 37, 38, 39, 40] by Arendt, ter Elst, and coauthors form an interesting series of papers on elliptic differential operators and Dirichlet-to-Neumann operators based mainly on form methods.”
- Friedlander's eigenvalue inequalities and the Dirichlet-to-Neumann semigroup (2012, background): “We mention also the recent paper [4] which considers a number of issues related to the ones here.”