Eikonal equations with discontinuities (Q1901094)

The authors consider the equation \(H(Du)= n(x)\) over an \(n\)-dimensional domain, where \(H\) is a convex functional, \(Du\) represents the \(x\)-gradient of \(u\) and \(n(x)\) is lower semicontinuous. A new notion of generalized solution for the problem under consideration is introduced and investigated from the variational approach. In particular, existence, uniqueness, stability and some comparison results are established for Dirichlet boundary conditions.