Approximation of diffuse measures for parabolic capacities

Petitta, Francesco;Porretta, Alessio;Ponce, Augusto
(2008) Comptes rendus - Mathématique — Vol. 346, n° 3-4, p. 161-166 (2008)

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  • Petitta, Francesco
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  • Porretta, Alessio
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  • Ponce, Augustoorcid-logoUCLouvain
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Abstract
Given a parabolic cylinder Q = (0, T) x Omega, with Omega subset of R-N, 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 v(t) - Delta(p)v with v is an element of L-p(0, T; W-0(1,p) (Omega)) boolean AND L-infinity (Q). Estimates on the capacity of level sets of solutions of parabolic equations play a crucial role in our proof.
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Petitta, F., Porretta, A., & Ponce, A. (2008). Approximation of diffuse measures for parabolic capacities. Comptes rendus - Mathématique, 346(3-4), 161-166. https://doi.org/10.1016/j.crma.2007.12.002 (Original work published 2008)