Abstract
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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