Abstract
We establish an Oleinik-type inequality concerning BV entropy solutions of general scalar conservation laws in one dimension: [Formula: see text] This inequality reads, for x ≤ y and t > 0: [Formula: see text] This contains Oleinik's inequality for convex fluxes; in particular, almost convex and almost concave fluxes yield solutions that almost satisfy Oleinik's estimate. We also show that this inequality is not satisfied in general when one replaces the factor [Formula: see text] with ‖(f″)-‖∞or with ‖(f″)+‖∞.
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