Poisson-transmission problems for \(L^\infty\)-perturbations of the Stokes system on Lipschitz domains in compact Riemannian manifolds

DOI10.1007/s10884-014-9359-0zbMath1381.58008OpenAlexW2460148074WikidataQ115383535 ScholiaQ115383535MaRDI QIDQ282372

Wolfgang L. Wendland, Cornel Pintea, Mirela Kohr

Publication date: 12 May 2016

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-014-9359-0

zbMATH Keywords

Sobolev spacesRiemannian manifoldsemilinear problemLipschitz domainBrinkman systemlayer potentialsPoisson-transmission problem

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Elliptic equations on manifolds, general theory (58J05)

Related Items (2)

Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian manifolds ⋮ On the transmission problems for the Oseen and Brinkman systems on Lipschitz domains in compact Riemannian manifolds

Cites Work

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• Integral equation method for the first and second problems of the Stokes system
• The Neumann problem for the planar Stokes system
• Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains
• Boundary value problems for the systems of elastostatics in Lipschitz domains
• Boundary integral equations
• Solution of the transmission problem
• Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
• Boundary layer methods for Lipschitz domains in Riemannian manifolds
• Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem
• Elliptic partial differential equations of second order
• The stationary Navier-Stokes system in nonsmooth manifolds: the Poisson problem in Lipschitz and \(C^{1}\) domains
• The Dirichlet problem for the Stokes system on Lipschitz domains
• Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains.
• Function spaces in Lipschitz domains and on Lipschitz manifolds. Characteristic functions as pointwise multipliers.
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Nonlinear Neumann-transmission problems for Stokes and Brinkman equations on Euclidean Lipschitz domains
• The Stokes operator with Neumann boundary conditions in Lipschitz domains
• Poisson problems for semilinear Brinkman systems on Lipschitz domains in \(\mathbb{R}^n\)
• Brinkman-type operators on Riemannian manifolds: Transmission problems in Lipschitz and \(C ^{1}\) domains
• The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains
• On the Robin Boundary Condition for Laplace's Equation in Lipschitz Domains
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Orientation and the Leray-Schauder theory for fully nonlinear elliptic boundary value problems
• EXISTENCE AND UNIQUENESS FOR A SEMILINEAR ELLIPTIC PROBLEM ON LIPSCHITZ DOMAINS IN RIEMANNIAN MANIFOLDS
• Existence and uniqueness for a semilinear elliptic problem on Lipschitz domains in Riemannian manifolds II
• Layer Potential Analysis for Pseudodifferential Matrix Operators in Lipschitz Domains on Compact Riemannian Manifolds: Applications to Pseudodifferential Brinkman Operators
• Navier-Stokes equations on Lipschitz domains in Riemannian manifolds.

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