Solvability conditions for the Neumann problem for the homogeneous polyharmonic equation

DOI10.1134/S0012266114110032zbMath1319.35032OpenAlexW2060760434WikidataQ115251560 ScholiaQ115251560MaRDI QIDQ2345781

Valery V. Karachik

Publication date: 21 May 2015

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266114110032

zbMATH Keywords

solvability conditionsNeumann problempolyharmonic equation

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (17)

On the solvability of some boundary value problems for the inhomogeneous polyharmonic equation with boundary operators of the Hadamard type ⋮ Sufficient conditions for solvability of one class of Neumann-type problems for the polyharmonic equation ⋮ Solving a problem of Robin type for biharmonic equation ⋮ Riquier-Neumann problem for the polyharmonic equation in a ball ⋮ Generalized third boundary value problem for the biharmonic equation ⋮ Integral identities on a sphere for normal derivatives of polyharmonic functions ⋮ On the Fredholm property and index of the generalized Neumann problem ⋮ Unnamed Item ⋮ Neumann type problems for the polyharmonic equation in ball ⋮ Class of Neumann-type problems for the polyharmonic equation in a ball ⋮ A Neumann-type problem for the biharmonic equation ⋮ Unnamed Item ⋮ On solvability of a boundary value problem for an inhomogeneous polyharmonic equation with a fractional order boundary operator ⋮ Regularized solution of an ill-posed biharmonic equation ⋮ On One Mathematical Model Described by Boundary Value Problem for the Biharmonic Equation ⋮ On Solvability of Some Boundary Value Problems with Involution for the Biharmonic Equation ⋮ On solvability of some boundary value problems for a biharmonic equation with periodic conditions

Cites Work

• Convergence of a class of deficient interpolatory splines
• Polynomial solutions of the Dirichlet problem for the biharmonic equation in the ball
• On some special polynomials
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