Adjoint boundary value problems for the biharmonic equation on \(C^ 1\) domains in the plane
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.
scientific article; zbMATH DE number 3971266