Erratum to: The Dirichlet problem associated to the relativistic heat equation

Abstract

In the original article we proved existence and uniqueness of entropy solutions for the nonhomogeneous Dirichlet problem associated to the relativistic heat equation. In the proof of uniqueness of both elliptic and parabolic entropy solutions (Theorems 2 and 3, respectively) we used that sign0 (u− u)u ∈ BV ( ) for two entropy solutions u, u. However, we did not prove this but we wrongly stated that this was true for any given functions u, u ∈ TBV( ), which is not the case, in general. The expression sign0 (u − u)u appears in the process of applying the doubling variables method, known as Kruzhkov’s method, if one lets the parameter e → 0+, which serves to approximate the sign function, before joining the space variables. In this note, we correct the aforementioned mistake by joining first the space variables and at the very end, letting e → 0+.