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- W3163252009 abstract "Abstract We consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$mathrm {C}(partial M)$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>(</mml:mo> <mml:mi>∂</mml:mi> <mml:mi>M</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> of continuous functions on the boundary $$partial M$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>∂</mml:mi> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> of a compact manifold $$overline{M}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mover> <mml:mi>M</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> with boundary. We prove that it generates an analytic semigroup of angle $$frac{pi }{2}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mfrac> <mml:mi>π</mml:mi> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> , 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 $$frac{pi }{2}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mfrac> <mml:mi>π</mml:mi> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> on the space $$mathrm {C}(overline{M})$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>C</mml:mi> <mml:mo>(</mml:mo> <mml:mover> <mml:mi>M</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> ." @default.
- W3163252009 created "2021-05-24" @default.
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- W3163252009 date "2021-05-18" @default.
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- W3163252009 title "Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds" @default.
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- W3163252009 doi "https://doi.org/10.1007/s00233-021-10192-z" @default.
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