Generation of Analytic Semigroups by Variational Operators with L ∞ Coefficients

Author(s):  
Vincenzo Vespri
Keyword(s):  
2021 ◽  
Author(s):  
Tim Binz

AbstractWe 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 ¯ ) .


1988 ◽  
Vol 61 (3) ◽  
pp. 235-255 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Vincenzo Vespri

Author(s):  
Robert H. Martin ◽  
Toshitaka Matsumoto ◽  
Shinnosuke Oharu ◽  
Naoki Tanaka

2007 ◽  
Vol 75 (2) ◽  
pp. 470-476 ◽  
Author(s):  
Wolfgang Desch ◽  
Gudrun Schappacher ◽  
Wilhelm Schappacher

2017 ◽  
Vol 18 (2) ◽  
pp. 269-294 ◽  
Author(s):  
Mark Elin ◽  
David Shoikhet ◽  
Nikolai Tarkhanov

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