Annales Mathematiques Africaines


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A Sobolev Inequality for Functions with Locally Bounded Variation in $\QTR{Bbb}{R}^{d}$



DOUYON Domion
D.E.R Mathématiques et Informatique
BP E 3206 BAMAKO, MALI


FOFANA Ibrahim
UFR Mathématiques et Informatique
Université de Cocody, 22 BP 582 Abidjan 22, Côte d'Ivoire

Abstract:


We prove a Sobolev type inequality for functions which partial derivatives in the sense of distribution have total variation in some amalgam space of measures.The proof is based on a trace theorem for Riesz potentials of Radon measures written in the form of an Olsen type inequality. We use this Sobolev inequality to obtain regularity conditions for solution of

MATH

where the data $\mu $ is a nonnegative Radon measure.

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