Solution of the Dirichlet problem with polynomial data for the polyharmonic equation in a ball

DOI10.1134/S0012266115080078zbMath1331.35118OpenAlexW2206649249WikidataQ115251463 ScholiaQ115251463MaRDI QIDQ897034

Valery V. Karachik

Publication date: 16 December 2015

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

Full work available at URL: https://doi.org/10.1134/s0012266115080078

zbMATH Keywords

Dirichlet boundary conditionunit ballpolyharmonic operatorpolynomial data

Mathematics Subject Classification ID

Biharmonic and polyharmonic equations and functions in higher dimensions (31B30) Higher-order elliptic equations (35J30)

Related Items (18)

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 ⋮ Generalized third boundary value problem for the biharmonic equation ⋮ Solutions of the generalized Dirichlet problem for the iterated slice Dirac equation ⋮ The Green function of the Dirichlet problem for the triharmonic equation in the ball ⋮ 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 ⋮ SOLVABILITY CONDITIONS OF THE N2 NEUMANN-TYPE PROBLEM FOR POLYHARMONIC EQUATION IN A BALL ⋮ On representations of real analytic functions by monogenic functions ⋮ Green's function of Dirichlet problem for biharmonic equation in the ball ⋮ On the Green’s Function for the Third Boundary Value Problem ⋮ The Green function of the Dirichlet problem for the biharmonic equation in a ball ⋮ ON REPRESENTATION OF GREEN’S FUNCTION OF THE DIRICHLET PROBLEM FOR BIHARMONIC EQUATION IN A BALL ⋮ On Green's function of the Robin problem for the Poisson equation ⋮ On a generalization of the initial-boundary problem for the vibrating string equation ⋮ On solvability of some boundary value problems for a biharmonic equation with periodic conditions

Cites Work

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• Real Bargmann spaces, Fischer decompositions, and sets of uniqueness for polyharmonic functions
• On an expansion of Almansi type
• Construction of polynomial solutions to some boundary value problems for Poisson’s equation
• On the mean value property for polyharmonic functions in the ball
• On one representation of analytic functions by harmonic functions
• Problème de l'analyticité par rapport à un opérateur linéaire
• Dirichlet's Problem When the Data is an Entire Function
• On solvability conditions for the Neumann problem for a polyharmonic equation in the unit ball

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