Adjoint boundary value problems for the biharmonic equation on \(C^ 1\) domains in the plane

DOI10.1007/BF02384427zbMath0602.35028MaRDI QIDQ1081746

B. George

Publication date: 1985

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

biharmonic equationsthin plateadjoint boundary value problemsinterior Dirichlet problemmultiple layer potential solutions

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Membranes (74K15) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items

Stress potentials on \(C^ 1\) domains ⋮ Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey ⋮ Maximum principles for the polyharmonic equation on Lipschitz domains ⋮ The Dirichlet problem for higher order equations in composition form ⋮ Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions ⋮ The Neumann problem for higher order elliptic equations with symmetric coefficients ⋮ The Ẇ−1,p Neumann problem for higher order elliptic equations ⋮ Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces ⋮ Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients ⋮ Dirichlet and Neumann boundary values of solutions to higher order elliptic equations ⋮ Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains

Cites Work

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• On the Hardy space-H of a \(C^ 1\) domain
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Potential techniques for boundary value problems on \(C^1\)-domains
• Multiple layer potentials and the dirichlet problem for higher order elliptic equations in the plane I
• Cauchy integrals on Lipschitz curves and related operators