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Regularity of the moments of the solution of a Transport Equation

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Date
1988
Dewey
Analyse
Sujet
Transport Equation
Journal issue
Journal of Functional Analysis
Volume
76
Number
1
Publication date
1988
Article pages
110-125
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/0022-1236(88)90051-1
URI
https://basepub.dauphine.fr/handle/123456789/13328
Collections
  • CEREMADE : Publications
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Author
Golse, François
Lions, Pierre-Louis
Perthame, Benoît
Sentis, Rémi
Type
Article accepté pour publication ou publié
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.

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