Barles, G.; Lions, P. L. Remarks on existence and uniqueness results for first-order Hamilton-Jacobi equations. (English) Zbl 0644.35015 Contributions to nonlinear partial differential equations, Vol. II, Proc. 2nd Franco-Span. Colloq., Paris 1985, Pitman Res. Notes Math. Ser. 155, 4-15 (1987). [For the entire collection see Zbl 0614.00011.] This 1987 paper generalizes some hypotheses regarding the hamiltonian for first order Hamilton-Jacobi equations. Thus, it considers the Dirichlet problem \(H(x,u,Du)=0\) in \(\Omega\) with \(u=\phi\) on the boundary of \(\Omega\). The objective is to prove existence and uniqueness of a bounded, uniformly continuous viscosity solution. The Cauchy problem is also considered. Reviewer: E.Barron Cited in 2 Documents MSC: 35F20 Nonlinear first-order PDEs 35D05 Existence of generalized solutions of PDE (MSC2000) Keywords:hamiltonian; first order Hamilton-Jacobi equations; Dirichlet problem; existence; uniqueness; viscosity solution; Cauchy problem Citations:Zbl 0614.00011 PDFBibTeX XML