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Journal of Convex Analysis 10 (2003), No. 2, 437--444
Copyright Heldermann Verlag 2003

Summability of Solutions of Elliptic and Parabolic Quasilinear Equations with Measures as Data

Youcef Atik
Lab. des EDP Non Linéaires et Histoire des Mathématiques, Ecole Normale Supérieure, B.P. 92, 16050 Kouba, Alger, Algeria,

Mohammed Boukra
Faculté des Sciences, Dép. de Mathématiques, Oued Aïssi, Université de Tizi-Ouzou, Algeria

We give a result of summability of solution of elliptic and parabolic boundary and initial-boundary value problems associated with an operator of Leray-Lions type when the right-hand side and the initial condition are two bounded Radon measures. This work generalizes the results of papers by L. Boccardo and T. Gallouet [J. Convex Analysis 3 (1996) 361--365] and Li Feng-Quan and Li Guang-Wei [J. Convex Analysis 7 (2000) 203--208].

Keywords: Summability, quasilinear elliptic and parabolic equations, measures as data.

MSC 2000: 35D10, 35R05.

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