scholarly journals A note on a transmission problem for the Brinkman system and the generalized Darcy-Forchheimer-Brinkman system in Lipschitz domains in R3

2019 ◽  
Vol 64 (3) ◽  
pp. 399-412
Author(s):  
Andrei-Florin Albisoru ◽  
◽  
Keyword(s):  
Transmission Problem ◽  
Lipschitz Domains ◽  
Brinkman System

Dirichlet problem for a nonlinear generalized Darcy-Forchheimer-Brinkman system in Lipschitz domains

2014 ◽  
Vol 38 (17) ◽  
pp. 3615-3628 ◽  
Author(s):  
Teodor Groşan ◽  
Mirela Kohr ◽  
Wolfgang L. Wendland
Keyword(s):  
Dirichlet Problem ◽  
Lipschitz Domains ◽  
Brinkman System

scholarly journals On the explicit representation of the trace space $$H^{\frac{3}{2}}$$ and of the solutions to biharmonic Dirichlet problems on Lipschitz domains via multi-parameter Steklov problems

2021 ◽  
Author(s):  
Pier Domenico Lamberti ◽  
Luigi Provenzano
Keyword(s):  
Fourier Series ◽  
Dirichlet Problem ◽  
Lipschitz Domain ◽  
Spectral Properties ◽  
Explicit Representation ◽  
Lipschitz Domains ◽  
Dirichlet Problems ◽  
Trace Space ◽  
In Series ◽  
Definition Of

AbstractWe consider the problem of describing the traces of functions in $$H^2(\Omega )$$ H 2 ( Ω ) on the boundary of a Lipschitz domain $$\Omega $$ Ω of $$\mathbb R^N$$ R N , $$N\ge 2$$ N ≥ 2 . We provide a definition of those spaces, in particular of $$H^{\frac{3}{2}}(\partial \Omega )$$ H 3 2 ( ∂ Ω ) , by means of Fourier series associated with the eigenfunctions of new multi-parameter biharmonic Steklov problems which we introduce with this specific purpose. These definitions coincide with the classical ones when the domain is smooth. Our spaces allow to represent in series the solutions to the biharmonic Dirichlet problem. Moreover, a few spectral properties of the multi-parameter biharmonic Steklov problems are considered, as well as explicit examples. Our approach is similar to that developed by G. Auchmuty for the space $$H^1(\Omega )$$ H 1 ( Ω ) , based on the classical second order Steklov problem.

Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem

2020 ◽  
Vol 191 ◽  
pp. 111645
Author(s):  
Matteo Dalla Riva ◽  
Riccardo Molinarolo ◽  
Paolo Musolino
Keyword(s):  
Transmission Problem ◽  
Singularly Perturbed ◽  
Local Uniqueness

Weighted H p Spaces on Lipschitz Domains

1980 ◽  
Vol 102 (1) ◽  
pp. 129 ◽  
Author(s):  
Carlos E. Kenig
Keyword(s):  
Lipschitz Domains
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