Partial differential equations in domains with self-contact (Q910555)

Let \(\Omega\) be a Euclidean domain, \(\Gamma_ 1,\Gamma_ 2\subset \Omega\) be ``smooth'' surfaces of codimension 1, and \(\alpha\) : \(\Gamma_ 1\to \Gamma_ 2\) be a ``smooth'' application. Here second and fourth order partial differential equations are studied in \(\Omega\) under the constraints \[ (1)\quad v(\sigma)=v(\alpha (\sigma))\quad on\quad \Gamma_ 1 \] and, for fourth order equations, \[ (2)\quad \nabla v(\sigma)=\nabla v(\alpha (\sigma))\quad on\quad \Gamma_ 1; \] these yield special discontinuity conditions on \(\Gamma_ 1\) and \(\Gamma_ 2\). These constraints can correspond to non-standard geometrical structures, which have natural applications in engineering.