Mathematics

Minimax solutions are weak solutions of Cauchy problems for Hamilton-Jacobi equations, constructed from generating families (quadratic at infinity) of the geometric solutions. We describe a new construction of the minimax in terms of Morse theory, and we show its stability by small perturbations of the generating family. We consider the wave front corresponding to the geometric solution as the graph of a multi-valued solution of the Cauchy problem, and we give a geometric criterion to find the graph of the minimax.