Optimal Besov differentiability for entropy solutions of the Eikonal equation
Francesco Ghiraldin, Xavier Lamy
TL;DR
This paper investigates the regularity of entropy solutions to the Eikonal equation in a planar domain, establishing key equivalences among Besov regularity, entropy production, and kinetic formulation validity.
Contribution
It introduces new equivalences linking Besov regularity, entropy production, and kinetic formulations for solutions of the Eikonal equation.
Findings
Proves the equivalence between optimal Besov regularity and entropy production finiteness.
Establishes the validity of a kinetic formulation under certain regularity conditions.
Provides a comprehensive characterization of entropy solutions in the planar Eikonal equation context.
Abstract
In this paper we study the Eikonal equation in a bounded planar domain. We prove the equivalence among optimal Besov regularity, the finiteness of every entropy production and the validity of a kinetic formulation.
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