Geometric and viscosity solutions for the Cauchy Problem of first Order

Abstract

There are two kinds of solutions of the Cauchy problem of first order, the viscosity solution and the more geometric minimax solution and in general they are different. The aim of this article is to show how they are related: iterating the minimax procedure during shorter and shorter time intervals one approaches the viscosity solution. This can be considered as an extension to the contact framework of the result of Q.Wei in the symplectic case.