On the selection of a particular class of solutions to a system of eikonal equations

TL;DR

This paper introduces a variational approach to select solutions of a system of eikonal equations that minimizes the discontinuity set of the gradient, addressing the challenge of solution selection under boundary conditions.

Contribution

It proposes a novel variational method for choosing solutions to eikonal systems that reduces gradient discontinuities, advancing solution regularity understanding.

Findings

The method effectively minimizes the gradient discontinuity set.

It provides a new criterion for solution selection in eikonal systems.

The approach enhances the regularity properties of solutions.

Abstract

In this article we consider a system of eikonal equations with a Dirichlet boundary condition. We propose a variational method to select the class of solutions which minimize the discontinuity set of the gradient.