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arXiv · 2509.00977

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

Fabio Ancona·Laura Caravenna·Alexander J. Cliffe·Elio Marconi
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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.

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Fabio Ancona, Laura Caravenna, Alexander J. Cliffe, Elio Marconi. 2025-08-31. On the regularity of continuous solutions to multidimensional scalar conservation laws with bounded source. https://arxiv.org/abs/2509.00977

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