Newcomb, Richard T. II; Su, Jianzhong Eikonal equations with discontinuities. (English) Zbl 0854.35022 Differ. Integral Equ. 8, No. 8, 1947-1960 (1995). 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. Reviewer: L.P.Lebedev (Rostov-na-Donu) Cited in 10 Documents MSC: 35F30 Boundary value problems for nonlinear first-order PDEs 35D05 Existence of generalized solutions of PDE (MSC2000) Keywords:eikonal equation PDFBibTeX XMLCite \textit{R. T. Newcomb II} and \textit{J. Su}, Differ. Integral Equ. 8, No. 8, 1947--1960 (1995; Zbl 0854.35022)