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On the Dirichlet problem for vectorial Hamilton-Jacobi equations

TitleOn the Dirichlet problem for vectorial Hamilton-Jacobi equations
Publication TypeJournal Article
Year of Publication1998
AuthorsZagatti, S
JournalSIAM J. Math. Anal. 29 (1998) 1481-1491
Abstract

We give sufficient conditions for the existence of solutions to the Hamilton--Jacobi equations with Dirichlet boundary condition: $$ \\\\cases{ g(x,{\\\\hbox{\\\\rm det}}Du(x))=0, \\\\ & for a.e. $x\\\\in\\\\Omega,$\\\\cr u(x)=\\\\varphi(x), & for $x\\\\in\\\\partial\\\\Omega,$} $$ obtaining, in addition, an application to the theory of existence of minimizers for a class of nonconvex variational problems.

URLhttp://hdl.handle.net/1963/3512
DOI10.1137/S0036141097321279

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