scholarly journals Strictly elliptic operators with generalized Wentzell boundary conditions on continuous functions on manifolds with boundary

2020 ◽  
Vol 115 (1) ◽  
pp. 111-120
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Continuous Functions ◽  
Elliptic Operators ◽  
Manifolds With Boundary ◽  
Wentzell Boundary Conditions

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

2021 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Compact Manifold ◽  
Analytic Semigroup ◽  
Continuous Functions ◽  
Analytic Semigroups ◽  
Abstract Theory ◽  
Neumann Operator ◽  
Wentzell Boundary Conditions ◽  
Dirichlet To Neumann Operator

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 ¯ ) .

Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem

2010 ◽  
Vol 283 (4) ◽  
pp. 504-521 ◽  
Author(s):  
Angelo Favini ◽  
Gisèle Ruiz Goldstein ◽  
Jerome A. Goldstein ◽  
Enrico Obrecht ◽  
Silvia Romanelli
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operators ◽  
Analytic Semigroups ◽  
Wentzell Boundary Conditions

scholarly journals Nonsymmetric elliptic operators with Wentzell boundary conditions in general domains

2016 ◽  
Vol 15 (6) ◽  
pp. 2475-2487 ◽  
Author(s):  
Angelo Favini ◽  
Gisèle Ruiz Goldstein ◽  
Jerome Goldstein ◽  
Enrico Obrecht ◽  
Silvia Romanelli
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operators ◽  
Wentzell Boundary Conditions

scholarly journals Wentzell Boundary Conditions in the Nonsymmetric Case

2008 ◽  
Vol 3 (7) ◽  
pp. 143-147 ◽  
Author(s):  
A. Favini ◽  
G. R. Goldstein ◽  
J. A. Goldstein ◽  
S. Romanelli
Keyword(s):  
Boundary Conditions ◽  
Wentzell Boundary Conditions

scholarly journals Homogenization and norm-resolvent convergence for elliptic operators in a strip perforated along a curve

2016 ◽  
Vol 146 (6) ◽  
pp. 1115-1158 ◽  
Author(s):  
Denis Borisov ◽  
Giuseppe Cardone ◽  
Tiziana Durante
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Rate Of Convergence ◽  
Elliptic Operators ◽  
Resolvent Convergence ◽  
Order Elliptic Operator ◽  
Classical Boundary ◽  
Norm Resolvent Convergence ◽  
Operator Norms ◽  
Infinite Planar

We consider an infinite planar straight strip perforated by small holes along a curve. In such a domain, we consider a general second-order elliptic operator subject to classical boundary conditions on the holes. Assuming that the perforation is non-periodic and satisfies rather weak assumptions, we describe all possible homogenized problems. Our main result is the norm-resolvent convergence of the perturbed operator to a homogenized one in various operator norms and the estimates for the rate of convergence. On the basis of the norm-resolvent convergence, we prove the convergence of the spectrum.

Nonautonomous heat equations with generalized Wentzell boundary conditions

2003 ◽  
Vol 3 (2) ◽  
pp. 321-331 ◽  
Author(s):  
Jin Liang ◽  
Rainer Nagel ◽  
Ti-Jun Xiao
Keyword(s):  
Boundary Conditions ◽  
Heat Equations ◽  
Wentzell Boundary Conditions
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