Balanced split sets and Hamilton-Jacobi equations

Angulo Ardoy, Pablo; Guijarro, Luis
January 2011
Calculus of Variations & Partial Differential Equations;Jan2011, Vol. 40 Issue 1/2, p223
Academic Journal
We study the singular set of solutions to Hamilton-Jacobi equations with a Hamiltonian independent of u. In a previous paper, we proved that the singular set is what we called a balanced split locus. In this paper, we find and classify all balanced split loci, identifying the cases where the only balanced split locus is the singular locus, and the cases where this does not hold. This clarifies the relationship between viscosity solutions and the classical approach of characteristics, providing equations for the singular set. Along the way, we prove more structure results about the singular sets.


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