A limiting case for Velocity
نویسندگان
چکیده
We complete the theory of velocity averaging lemmas for transport equations by studying the limiting case of a full space derivative in the source term. Although the compactness of averages does not hold any longer, a speciic estimate remains, which shows compactness of averages in more general situations than those previously known. Our method is based on Calderon-Zygmund theory. R esum e Nous compl etons les lemmes de moyenne pour les equations de transport en etudiant le cas limite d'une d eriv ee en espace dans le terme source. La compacit e des moyennes ne peut ^ etre obtenue, mais nous d emontrons une estimation sp eciffque qui permet de montrer la com-pacit e en moyenne dans les situations les plus g en erales connues actuelle-ment. Notre m ethode s'appuie sur la th eorie de Calderon-Zygmund.
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