English

On the regularity of continuous solutions to multidimensional scalar conservation laws with bounded source

Analysis of PDEs 2025-09-03 v1

Abstract

We prove the H\"older 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.

Keywords

Cite

@article{arxiv.2509.00977,
  title  = {On the regularity of continuous solutions to multidimensional scalar conservation laws with bounded source},
  author = {Fabio Ancona and Laura Caravenna and Alexander J. Cliffe and Elio Marconi},
  journal= {arXiv preprint arXiv:2509.00977},
  year   = {2025}
}
R2 v1 2026-07-01T05:14:21.978Z