Analytic semigroups generated on hölder spaces by second order elliptic systems under Dirichlet boundary conditions

1985 ◽  
Vol 140 (1) ◽  
pp. 393-415 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Vincenzo Vespri
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Elliptic Systems ◽  
Second Order ◽  
Dirichlet Boundary Conditions ◽  
Analytic Semigroups ◽  
Hölder Spaces ◽  
Holder Spaces

The resolvent problem for the Stokes system in exterior domains: uniqueness and non-regularity in Hölder spaces

1992 ◽  
Vol 122 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
Paul Deuring
Keyword(s):  
Boundary Conditions ◽  
Existence Result ◽  
Stokes System ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Exterior Domains ◽  
Hölder Spaces ◽  
Image Position ◽  
Holder Spaces ◽  
Resolvent Problem

SynopsisWe consider the resolvent problem for the Stokes system in exterior domains, under Dirichlet boundary conditions:where Ω is a bounded domain in ℝ3. It will be shown that in general there is no constant C > 0 such that for with , div u = 0, and for with . However, if a solution (u, π) of problem (*) exists, it is uniquely determined, provided that u(x) and ∇π(x) decay for large values of |x|. These assertions imply a non-existence result in Hölder spaces.

scholarly journals Well Posedness for a Class of Flexible Structure in Hölder Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Claudio Cuevas ◽  
Carlos Lizama
Keyword(s):  
Boundary Conditions ◽  
External Force ◽  
Dirichlet Boundary ◽  
Flexible Structures ◽  
Dirichlet Boundary Conditions ◽  
Flexible Structure ◽  
Well Posedness ◽  
Hölder Spaces ◽  
Holder Spaces ◽  
Well Posed

We characterize well-posedness in Hölder spaces for an abstract version of the equation(∗) u′′+λu′′′=c2(Δu+μΔu′)+fwhich model thevibrationsof flexible structures possessing internal material damping and external forcef. As a consequence, we show that in case of the Laplacian with Dirichlet boundary conditions, equation(∗)is always well-posed provided0<λ<μ.

scholarly journals On Dirichlet boundary conditions in second-order FE2-schemes

PAMM ◽  
2010 ◽  
Vol 10 (1) ◽  
pp. 423-424
Author(s):  
Hans-Georg Sehlhorst ◽  
Alexander Düster ◽  
Ralf Jänicke ◽  
Stefan Diebels
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Second Order ◽  
Dirichlet Boundary Conditions
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