A variational approach in weighted Sobolev spaces to the operator \(- \Delta +\partial /\partial x_ 1\) in exterior domains of \({\mathbb{R}}^ 3\)

DOI10.1007/BF02571807zbMath0727.35041MaRDI QIDQ803393

Reinhard Farwig

Publication date: 1992

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174412

zbMATH Keywords

regularityDirichlet problemexistenceuniquenessweighted Sobolev spacesexterior domainOseen equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Navier-Stokes equations (35Q30) Variational methods for second-order elliptic equations (35J20)

Related Items

Dirichlet and Neumann exterior problems for the \(n\)-dimensional Laplace operator. An approach in weighted Sobolev spaces ⋮ Anisotropic weighted \(L^{p}\) spaces for the stationary exterior 3D-problem of Oseen ⋮ Weighted Sobolev spaces for the steady scalar Oseen equation in \(\mathbb R^n\) ⋮ Exterior Stationary Navier–Stokes Flows in 3D with Nonzero Velocity at Infinity: Asymptotic Behavior of the Second Derivatives of the Velocity ⋮ The stationary Navier-Stokes equations in 3D exterior domains. An approach in anisotropically weighted \(L^q\) spaces ⋮ \(L^p\)-inequalities for scalar Oseen potential ⋮ Anisotropic \(L^2\)-estimates of weak solutions to the stationary Oseen-type equations in 3D-exterior domain for a rotating body ⋮ On the Oseen fundamental solution and the asymptotic profile of flows past a translating object

Cites Work

• The stationary exterior 3D-problem of Oseen and Navier-Stokes equations in anisotropically weighted spaces
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• Lösungen der poissongleichung und harmonische vektorfelder in unbeschränkten gebieten
• The behavior of the laplacian on weighted sobolev spaces
• Boundary value problems for the laplacian in an exterior domain
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