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Strong Traces for Solutions of Multidimensional Scalar Conservation Laws

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Abstract

In this paper we consider multidimensional scalar conservation laws without BV estimates defined in a subset Ω⊂ℝ+×ℝd. We show that, with a non-degeneracy hypothesis on the flux, we can define a strong notion of trace at the boundary of Ω reached by L 1 convergence.

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  1. Laboratoire J.A.Dieudonné¶Université de Nice Sophia-Antipolis¶Parc Valrose,¶06108 Nice Cedex 02¶e-mail: vasseur@math.unice.fr, , , , , , FR

    Alexis Vasseur

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  1. Alexis Vasseur
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Accepted April 11, 2001¶Published online October 30, 2001

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Vasseur, A. Strong Traces for Solutions of Multidimensional Scalar Conservation Laws. Arch. Rational Mech. Anal. 160, 181–193 (2001). https://doi.org/10.1007/s002050100157

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  • DOI: https://doi.org/10.1007/s002050100157

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