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

Youcef Atik; Mohammed Boukra

Abstract

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].

Author information

Contact details are reproduced from the original publication and may be historical.

Youcef Atik

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

youcefatiq@hotmail.com

Mohammed Boukra

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

Keywords

Summability
quasilinear elliptic and parabolic equations
measures as data

Mathematics Subject Classification

35D10, 35R05

Suggested citation

Y. Atik, M. Boukra. “Summability of Solutions of Elliptic and Parabolic Quasilinear Equations with Measures as Data.” Journal of Convex Analysis 10 (2003), No. 2, 437–444.