Analyticity on L 1 of the heat semigroup with Wentzell boundary conditions

Warma, Mahamadi

doi:10.1007/s00013-009-0068-6

Cited by 9 publications

(6 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, additional efforts were needed to prove analyticity of the semigroup on C( ) and L 1 ( ) × L 1 (∂ ): this issue could only be settled in [21,55] when quite different techniques were first exploited. In particular, in [21] the authors applied in a smart way a theory of a certain class of operator matrices that has been developed by Engel beginning with [19].…”

Section: ∂ ) (Again (12) Is Obtained Taking the Trace Of The Firstmentioning

confidence: 99%

Asymptotics of semigroups generated by operator matrices

Mugnolo

2014

Arab. J. Math.

View full text Add to dashboard Cite

We survey some known results about operator semigroup generated by operator matrices with diagonal or coupled domain. These abstract results are applied to the characterization of well-/ill-posedness for a class of evolution equations with dynamic boundary conditions on domains or metric graphs. In particular, our results on the heat equation with general Wentzell-type boundary conditions complement those previously obtained by, among others, Bandle-von Below-Reichel and Vázquez-Vitillaro.

show abstract

Section: ∂ ) (Again (12) Is Obtained Taking the Trace Of The Firstmentioning

confidence: 99%

Asymptotics of semigroups generated by operator matrices

Mugnolo

2014

Arab. J. Math.

View full text Add to dashboard Cite

show abstract

“…Later Engel and Fragnelli [17] generalize this result to uniformly elliptic operators, however without specifying the corresponding angle of analyticity. For related work see also [11][12][13][14]22,23,38,39] and the references therein. Our interest in this context is the generation of an analytic semigroup with the optimal angle of analyticity.…”

Section: Introductionmentioning

confidence: 99%

Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

Binz

2021

Semigroup Forum

View full text Add to dashboard Cite

We consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions on the boundary $$\partial M$$ ∂ M of a compact manifold $$\overline{M}$$ M ¯ with boundary. We prove that it generates an analytic semigroup of angle $$\frac{\pi }{2}$$ π 2 , generalizing and improving a result of Escher with a new proof. Combined with the abstract theory of operators with Wentzell boundary conditions developed by Engel and the author, this yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $$\frac{\pi }{2}$$ π 2 on the space $$\mathrm {C}(\overline{M})$$ C ( M ¯ ) .

show abstract

“…This result has been extended in [4] to the case of the Laplace operator with Dirichlet boundary condition on an arbitrary open set Ω. The case of the Wentzell boundary condition has been investigated in [32]. Holomorphy on spaces of continuous functions has been also studied in [4,21,30,31,32] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Fractional Gaussian estimates and holomorphy of semigroups

2019

Self Cite

View full text Add to dashboard Cite

Let Ω ⊂ R N be an arbitrary open set and denote by (e −t(−∆) s R N ) t≥0 (where 0 < s < 1) the semigroup on L 2 (R N ) generated by the fractional Laplace operator. In the first part of the paper we show that if T is a self-adjoint semigroup on L 2 (Ω) satisfying a fractional Gaussian estimate in the sense, then T defines a bounded holomorphic semigroup of angle π 2 that interpolates on L p (Ω), 1 ≤ p < ∞. Using a duality argument we prove that the same result also holds on the space of continuous functions. In the second part, we apply the above results to realization of fractional order operators with the exterior Dirichlet conditions. 2010 Mathematics Subject Classification. 35R11, 47D06, 47D03.

show abstract

Analyticity on L 1 of the heat semigroup with Wentzell boundary conditions

Abstract: We show that the semigroup generated by the realization of the Laplace operator with Wentzell boundary conditions in a bounded smooth domain is analytic on L 1 (Ω) ⊕ L 1 (∂Ω). Mathematics Subject Classification (2000). Primary 35K05; Secondary 47D06.

Cited by 9 publications

References 9 publications

Asymptotics of semigroups generated by operator matrices

Asymptotics of semigroups generated by operator matrices

Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

Fractional Gaussian estimates and holomorphy of semigroups

Contact Info

Product

Resources

About