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Regularity of the moments of the solution of a Transport Equation

Golse, François; Lions, Pierre-Louis; Perthame, Benoît; Sentis, Rémi (1988), Regularity of the moments of the solution of a Transport Equation, Journal of Functional Analysis, 76, 1, p. 110-125. http://dx.doi.org/10.1016/0022-1236(88)90051-1

Type
Article accepté pour publication ou publié
Date
1988
Journal name
Journal of Functional Analysis
Volume
76
Number
1
Publisher
Elsevier
Pages
110-125
Publication identifier
Metadata
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Author(s)
Golse, François
Lions, Pierre-Louis
Perthame, Benoît cc
Sentis, Rémi
Abstract (EN)
Let u = u(x, v) satisfy the Transport Equation View the MathML source, x∈View the MathML sourceN, v∈View the MathML sourceNwhere f belongs to some space of type Lp(dx ⊗ dμ(v)) (where μ is a positive bounded measure on View the MathML sourceN). We study the resulting regularity of the moment ∝ u(x, v) dμ(v) (in terms of fractional Sobolev spaces, for example). Counter-examples are given in order to test the optimality of our results.
Subjects / Keywords
Transport Equation