Mean value formulas, Weyl's lemma and Liouville theorems for \(\Delta^ 2\) and Stokes' system

DOI10.1007/BF03323122zbMath0766.31006WikidataQ125056432 ScholiaQ125056432MaRDI QIDQ1205493

Christian G. Simader

Publication date: 1 April 1993

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Harnack's inequalitybiharmonic functionsWeyl's lemmaLiouville's theoremsmean value properly

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Variational methods for higher-order elliptic equations (35J35)

Related Items (10)

A note on the reflection principle for the biharmonic equation and the Stokes system ⋮ ON THE STOKES EQUATIONS: THE MAXIMUM MODULUS THEOREM ⋮ Isolated singularities of polyharmonic operator in even dimension ⋮ Compatible hereditary classes in GTS ⋮ Existence and regularity of steady-state solutions of the Navier-Stokes equations arising from irregular data ⋮ Unnamed Item ⋮ Equivalence of weak Dirichlet's principle, the method of weak solutions and Perron's method towards classical solutions of Dirichlet's problem for harmonic functions ⋮ Nonlinear biharmonic equation in half-space with rough Neumann boundary data and potentials ⋮ Deterministic ill-posedness and probabilistic well-posedness of the viscous nonlinear wave equation describing fluid-structure interaction ⋮ Asymptotic behavior of solutions of a biharmonic Dirichlet problem with large exponents

Cites Work

• Unnamed Item
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• On the Representation of Stokes Flows
• Elliptic Partial Differential Equations of Second Order

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