Comptes Rendus
Partial differential equations
On optimal regularity estimates for finite-entropy solutions of scalar conservation laws
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 599-608.

We consider finite-entropy solutions of scalar conservation laws u t +a(u) x =0, that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function a is strictly convex (with possibly degenerate convexity) and a forms a doubling measure, we obtain a characterization of finite-entropy solutions in terms of an optimal regularity estimate involving a cost function first used by Golse and Perthame.

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DOI: 10.5802/crmath.427
Classification: 35L65

Xavier Lamy 1; Andrew Lorent 2; Guanying Peng 3

1 Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS, UPSIMT, F-31062 Toulouse Cedex 9, France.
2 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA.
3 Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, USA.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Xavier Lamy; Andrew Lorent; Guanying Peng. On optimal regularity estimates for finite-entropy solutions of scalar conservation laws. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 599-608. doi : 10.5802/crmath.427. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.427/

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