Optimal Besov differentiability for entropy solutions of the Eikonal equation

Francesco Ghiraldin (1) , Xavier Lamy (2)

1 Department of Mathematics [Basel]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Domaines: Equations aux dérivées partielles [math.AP]

Francesco Ghiraldin, Xavier Lamy. Optimal Besov differentiability for entropy solutions of the Eikonal equation. Communications on Pure and Applied Mathematics, 2020, 73 (2), pp.317-349. ⟨10.1002/cpa.21868⟩. ⟨hal-01701797⟩