Bounded solutions of the Dirichlet problem for the Stokes resolvent system

DOI10.1080/17476933.2016.1200565zbMath1347.35204OpenAlexW2460875180MaRDI QIDQ2816608

Dagmar Medková

Publication date: 25 August 2016

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2016.1200565

zbMATH Keywords

Dirichlet problemBrinkman systemlayer potential operatorsmaximum modulus principle

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Stokes and related (Oseen, etc.) flows (76D07) Maximum principles in context of PDEs (35B50) Second-order elliptic systems (35J47)

Related Items (6)

Classical solutions of the Dirichlet problem for the Darcy-Forchheimer-Brinkman system ⋮ The Robin problem for the Brinkman system and for the Darcy-Forchheimer-Brinkman system ⋮ \(L^q\)-solution of the Robin problem for the Stokes system with Coriolis force ⋮ Layer potentials and Poisson problems for the nonsmooth coefficient Brinkman system in Sobolev and Besov spaces ⋮ Classical solutions of the Robin problem for the Darcy-Forchheimer-Brinkman system ⋮ Boundary value problems for the Brinkman system with \(L^\infty\) coefficients in Lipschitz domains on compact Riemannian manifolds. A variational approach

Cites Work

• Unnamed Item
• Unnamed Item
• The inhomogeneous Dirichlet problem for the Stokes system in Lipschitz domains with unit normal close to VMO
• Very weak solutions to the stationary Stokes and Stokes resolvent problem in weighted function spaces
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• An extremal problem related to the maximum modulus theorem for Stokes functions
• The maximum modulus theorem for the Stokes system in a ball
• Weighted \(L^q\)-theory for the Stokes resolvent in exterior domains
• Elliptic partial differential equations of second order
• The Dirichlet problem for the Stokes system on Lipschitz domains
• Generalized resolvent estimates for the Stokes system in bounded and unbounded domains
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Maximal \(L^p\)-\(L^ q\)-estimates for the Stokes equation: a short proof of Solonnikov's theorem
• Nonlinear Neumann-transmission problems for Stokes and Brinkman equations on Euclidean Lipschitz domains
• Boundary value problems of Robin type for the Brinkman and Darcy-Forchheimer-Brinkman systems in Lipschitz domains
• Resolvent estimates in \(L ^{p }\) for the Stokes operator in Lipschitz domains
• Poisson problems for semilinear Brinkman systems on Lipschitz domains in \(\mathbb{R}^n\)
• Transmission problem for the Brinkman system
• The boundary value problems of the Stokes resolvent equations inn dimensions
• The resolvent problem for the stokes system in exterior domains: An elementary approach
• A generalization of Dahlberg's theorem concerning the regularity of harmonic Green potentials
• Stokes problem for Lipschitz domain
• ON THE STOKES EQUATIONS: THE MAXIMUM MODULUS THEOREM
• On the maximum modulus theorem for stokes functions
• The Dirichlet problems for the Stokes resolvent equations in bounded and exterior domains in ℝⁿ
• The $L^p$ Dirichlet problem for the Stokes system on Lipschitz domains
• Navier-Stokes equations on Lipschitz domains in Riemannian manifolds.
• Integral representation of a solution of the Neumann problem for the Stokes system

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