On gradient flows
The purpose of this paper is to contribute to the theory of existence of solutions to ordinary differential equations in \(\mathbb{R}^n\), when the right hand side of the equation is not necessarily continuous. More precisely the authors study existence and uniqueness of solutions for the equation \(x'= \nabla u(x)\) when \(u\) is not necessarily differentiable everywhere. This problem is closely related with (multidimensional) calculus of variations.
scientific article; zbMATH DE number 1206630
scientific article