Our objective is to establish a generalized Oleinik-type inequality for a convex scalar balance law with nonlinear source term [Formula: see text], in the spirit of the classical results obtained independently by Lax and Oleinik for scalar conservation laws. From this inequality, and under a generic condition linking the flux function and the source term, we deduce a [Formula: see text] regularity result for the unique entropy solution. If this condition is not satisfied, we obtain instead a fractional regularity result, showing that the solution lies in [Formula: see text] for some [Formula: see text], as in the homogeneous case [Formula: see text].
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Harb et al. (2026) studied this question.
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