We consider finite-entropy solutions of scalar conservation laws , that is, bounded weak solutions whose entropy productions are locally finite Radon measures. Under the assumptions that the flux function is strictly convex (with possibly degenerate convexity) and 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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Xavier Lamy 1; Andrew Lorent 2; Guanying Peng 3
@article{CRMATH_2023__361_G3_599_0, author = {Xavier Lamy and Andrew Lorent and Guanying Peng}, title = {On optimal regularity estimates for finite-entropy solutions of scalar conservation laws}, journal = {Comptes Rendus. Math\'ematique}, pages = {599--608}, publisher = {Acad\'emie des sciences, Paris}, volume = {361}, year = {2023}, doi = {10.5802/crmath.427}, language = {en}, }
TY - JOUR AU - Xavier Lamy AU - Andrew Lorent AU - Guanying Peng TI - On optimal regularity estimates for finite-entropy solutions of scalar conservation laws JO - Comptes Rendus. Mathématique PY - 2023 SP - 599 EP - 608 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.427 LA - en ID - CRMATH_2023__361_G3_599_0 ER -
%0 Journal Article %A Xavier Lamy %A Andrew Lorent %A Guanying Peng %T On optimal regularity estimates for finite-entropy solutions of scalar conservation laws %J Comptes Rendus. Mathématique %D 2023 %P 599-608 %V 361 %I Académie des sciences, Paris %R 10.5802/crmath.427 %G en %F CRMATH_2023__361_G3_599_0
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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