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On optimal regularity estimates for finite-entropy solutions of scalar conservation laws
Lamy, Xavier1  ; Lorent, Andrew2 ; Peng, Guanying3
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.
Comptes Rendus. Mathématique, Tome 361 (2023) no. G3, pp. 599-608

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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

Lamy, Xavier 1 ; Lorent, Andrew 2 ; Peng, Guanying 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.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {On optimal regularity estimates for finite-entropy solutions of scalar conservation laws},
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     pages = {599--608},
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Lamy, Xavier; Lorent, Andrew; Peng, Guanying. On optimal regularity estimates for finite-entropy solutions of scalar conservation laws. Comptes Rendus. Mathématique, Tome 361 (2023) no. G3, pp. 599-608. doi: 10.5802/crmath.427

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