Calculus of Variations and Geometric Measure Theory

F. Ancona - L. Caravenna - A. Cliffe - E. Marconi

On the regularity of continuous solutions to multidimensional scalar conservation laws with $L^\infty$ source

created by marconi on 11 Sep 2025

[BibTeX]

Preprint

Inserted: 11 sep 2025
Last Updated: 11 sep 2025

Year: 2025
Links: arXiv

Abstract:

We prove the Hölder regularity of continuous isentropic solutions to multi-dimensional scalar balance laws when the source term is bounded and the flux satisfies general assumptions of nonlinearity. The results are achieved by exploiting the kinetic formulation of the balance law.


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