Analyticity of the Dirichlet-to-Neumann semigroup on continuous functions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-03

AUTHORS

A. F. M. ter Elst, E. M. Ouhabaz

ABSTRACT

Let Ω be a bounded open subset with C1+κ-boundary for some κ>0. Consider the Dirichlet-to-Neumann operator associated with the elliptic operator -∑∂l(ckl∂k)+V, where the ckl=clk are Hölder continuous and V∈L∞(Ω) are real valued. We prove that the Dirichlet-to-Neumann operator generates a C0-semigroup on the space C(∂Ω) which is in addition holomorphic with angle π2. We also show that the kernel of the semigroup has Poisson bounds on the complex right half-plane. As a consequence, we obtain an optimal holomorphic functional calculus and maximal regularity on Lp(Γ) for all p∈(1,∞). More... »

PAGES

21-31

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00028-018-0467-x

DOI

http://dx.doi.org/10.1007/s00028-018-0467-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1106469985


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