A note on the reflection principle for the biharmonic equation and the Stokes system

DOI10.1007/BF00995128zbMath0815.31002MaRDI QIDQ1341885

Reinhard Farwig

Publication date: 11 January 1995

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

zbMATH Keywords

uniqueness theorembiharmonic equationStokes systemuniqueness of weak solutionsreflection principleweighted \(L^ q\)-spaces

Mathematics Subject Classification ID

Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30)

Related Items (17)

Nonhomogeneous biharmonic problem in the half-space, \(L^{p}\) theory and generalized solutions ⋮ Steklov-Farwig biharmonic problem in exterior domains ⋮ Optimal three spheres inequality at the boundary for the Kirchhoff-Love plate's equation with Dirichlet conditions ⋮ On the biharmonic problem with the Steklov-type and Farwig boundary conditions ⋮ On non-local reflection for elliptic equations of the second order in $\mathbb{R}^{2}$ (the Dirichlet condition) ⋮ On the vorticity of the Oseen problem in a half plane ⋮ Dirichlet-Neumann problem for the biharmonic equation in exterior domains ⋮ On the polyharmonic Neumann problem in weighted spaces ⋮ On solutions of a boundary value problem for the biharmonic equation ⋮ Weighted \(L^p\) theory of the Stokes and the bilaplacian operators in the half-space ⋮ On the dependence of the reflection operator on boundary conditions for biharmonic functions ⋮ On a generalized Stokes system with slip boundary conditions in the half-space ⋮ Biharmonic Dirichlet-Farwig problem in exterior domains ⋮ Uniqueness and factorization method for inverse elastic scattering with a single incoming wave ⋮ On the Steklov-type biharmonic problem in unbounded domains ⋮ Exterior Stokes problem in the half-space ⋮ Mixed Biharmonic Dirichlet-Neumann Problem in Exterior Domains

Cites Work

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• Existence, uniqueness and asymptotics of steady jets
• Mean value formulas, Weyl's lemma and Liouville theorems for \(\Delta^ 2\) and Stokes' system
• Generalized resolvent estimates for the Stokes system in bounded and unbounded domains
• Continuation of biharmonic functions by reflection
• On the reflection principle for polyharmonic functions
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I

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