TER ELST, A.F.M.; OUHABAZ, El Maati

doi:10.1007/s00028-018-0467-x

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TER ELST, A.F.M.

OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

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Journal of Evolution Equations. 2019-03, vol. 19, n° 1, p. 21-31

Springer Verlag

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Let Ω be a bounded open subset with C 1+κ-boundary for some κ > 0. Consider the Dirichlet-to-Neumann operator associated to the elliptic operator − ∂ l (c kl ∂ k) + V , where the c kl = c lk are Hölder continuous and V ∈ L ∞ (Ω) are real valued. We prove that the Dirichlet-to-Neumann operator generates a C 0-semigroup on the space C(∂Ω) which is in addition holomorphic with angle π 2. 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 L p (Γ) for all p ∈ (1, ∞).< Leer menos

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C 0 -semigroup

Poisson bounds

holomorphic semigroup Home institutions:

AMS Subject Classification: 47D06

35K08 Keywords: Dirichlet-to-Neumann operator

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Analyticity of the Dirichlet-to-Neumann semigroup on continuous functions

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