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• W2783454568 abstract "In this paper we relate the generator property of an operator $A$ with (abstract) generalized Wentzell conditions on a Banach space $X$ and its associated (abstract) Dirichlet-to-Neumann operator $N$ acting on a boundary space $partial X$. Our approach is based on similarity transformations and perturbation arguments and allows to split $A$ into an operator $A_{00}$ with Dirichlet-type conditions on a space $X_0$ of states having zero and the operator $N$. If $A_{00}$ generates an analytic semigroup, we obtain under a weak Hille--Yosida type condition that $A$ generates an analytic semigroup on $X$ if and only if $N$ does so on $partial X$. Here we assume that the (abstract) trace operator $L:Xtopartial X$ is bounded what is typically satisfied if $X$ is a space of continuous functions. Concrete applications are made to various second order differential operators." @default.
• W2783454568 created "2018-01-26" @default.
• W2783454568 creator A5040709326 @default.
• W2783454568 creator A5061599810 @default.
• W2783454568 date "2018-01-16" @default.
• W2783454568 modified "2023-09-27" @default.
• W2783454568 title "Operators with Wentzell boundary conditions and the Dirichlet-to-Neumann operator" @default.
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• W2783454568 hasPublicationYear "2018" @default.
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