A varifold solution to the nonlinear equation of motion of a vibrating membrane
The authors study the ``minimal surface-wave-equation'' \[ u_{tt}- \nabla \cdot (\nabla u/\sqrt{1+| \nabla u|^ 2})=0 \] in \(\Omega \subset {\mathbb{R}}^ n\) with homogeneous boundary conditions and suitable initial conditions in the setting of geometric measure theory, especially in the framework of varifolds. They prove existence of a global varifold solution and study the relation between varifold- and BV-solutions.
scientific article; zbMATH DE number 4026224