Necessary and Sufficient Condition for the Existenceof a Classical Solution of the InhomogeneousBiharmonic Equation

We prove that a necessary and sufficient condition for the existence of a classical solution of the inhomogeneous biharmonic equation in a bounded plane domain is the requirement of stronger continuity of the function on the right-hand side in the equation.

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Bibliographic Details
Published in:Differential equations 2021-01, Vol.57 (3), p.304-316
Main Authors: Grishanina, G E, Mukhamadiev, E M
Format: Article
Language:English
Subjects:
Biharmonic equations
Continuity (mathematics)
Differential equations
Mathematics
Online Access:Get full text
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Description
Summary:We prove that a necessary and sufficient condition for the existence of a classical solution of the inhomogeneous biharmonic equation in a bounded plane domain is the requirement of stronger continuity of the function on the right-hand side in the equation.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266121030046