%0 Journal Article %D 2014 %T Maximal generalized solution of eikonal equation %A Sandro Zagatti %X We study the Dirichlet problem for the eikonal equation: 1/2 |∇u(x)|^2-a(x)=0 in Ω u(x)=(x) on Ω, without continuity assumptions on the map a(.). We find a class of maps a(.) contained in the space L∞(Ω) for which the problem admits a (maximal) generalized solution, providing a generalization of the notion of viscosity solution. %I Elsevier %G en %U http://urania.sissa.it/xmlui/handle/1963/34642 %1 34846 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-21T08:38:44Z (GMT) No. of bitstreams: 0 %R 10.1016/j.jde.2014.04.001