Adjoint boundary value problems for the biharmonic equation on \(C^ 1\) domains in the plane
type: Item
instance of: scholarly article
title: Adjoint boundary value problems for the biharmonic equation on \(C^ 1\) domains in the plane
zbMATH Open document ID: 0602.35028
DOI: 10.1007/BF02384427
author: B. George
published in: Arkiv för Matematik
publication date: 1985-01-01T00:00:00Z
review text: The authors study adjoint boundary value problems for the biharmonic equations in a bounded \(C^ 1\) domain in \(R^ 2\), i.e. to solve the following problem: \[ (1)\quad \Delta^ 2v=0\quad in\quad \Omega;\quad (v_{xx}x_ s+v_{xy}y_ s,\quad v_{xy}x_ s+v_{yy}y_ s)=(\phi,\psi)\quad on\quad \partial \Omega. \] The method is to obtain multiple layer potential solutions to the interior Dirichlet problem for the biharmonic equation. Problem (1) is equivalent to finding the stress function from the x and y components of normal stress on the boundary of a thin plate, a fundamental problem in the theory of two dimensional elasticity.
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 74K15
zbMATH DE Number: 3971266
zbMATH Keywords: adjoint boundary value problems
zbMATH Keywords: biharmonic equations
zbMATH Keywords: multiple layer potential solutions
zbMATH Keywords: interior Dirichlet problem
zbMATH Keywords: thin plate
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3971266