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Comptes Rendus Mathématique
Volume 346, n° 3-4
pages 161-166 (février 2008)
Doi : 10.1016/j.crma.2007.12.002
accepted : 25 November 2007
Approximation of diffuse measures for parabolic capacities
Approximation des mesures diffuses pour des capacités paraboliques
 

Francesco Petitta a , Augusto C. Ponce b , Alessio Porretta c
a Dipartimento di Matematica, Università di Roma La Sapienza, Piazzale A. Moro 2, 00185 Roma, Italy 
b Laboratoire de mathématiques et physique théorique (CNRS UMR 6083), Université de Tours, 37200 Tours, France 
c Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy 

Abstract

Given a parabolic cylinder  , with  , we consider the class of finite measures which do not charge sets of zero p -parabolic capacity in Q . We prove that such measures can be strongly approximated by measures which can be written as   with  . Estimates on the capacity of level sets of solutions of parabolic equations play a crucial role in our proof. To cite this article: F. Petitta et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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Résumé

Étant donné un cylindre parabolique  , avec  , on considère la classe des mesures bornées sur Q qui ne chargent pas les ensembles de p -capacité nulle. Nous démontrons que ces mesures peuvent être approchées au sens fort par des mesures de la forme   avec  . Des estimations sur la capacité des ensembles de niveau des solutions d’équations paraboliques jouent un rôle crucial dans notre preuve. Pour citer cet article : F. Petitta et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

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