Patrizia Donato, Daniela Giachetti
Université de Rouen
Laboratoire de Mathématiques Raphaël Salem
UMR 6085 CNRS
Avenue de L'Université, BP 12
76801, St Etienne du Rouvray, FRANCE
Università degli Studi di Roma ``La Sapienza"
Dipartimento di Scienze di Base e Applicate per l'Ingegneria
Via Scarpa 14, 00161, Roma, ITALY

Abstract. The paper deals with the asymptotic behaviour of the solutions of quasilinear elliptic Dirichlet problems when the (linear) principal parts H-converge and the lower order terms exhibit a natural growth in the gradient variable and a singular behaviour in the variable. The lower order term in the limit problem presents the same singularity in the variable and the same growth in the gradient variable. The quadratic nonlinearity in the gradient is constructed through the correctors associated to the principal parts, on which natural integrability hypotheses are assumed.

Received: December 1, 2011

AMS Subject Classification: 35Jxx

Key Words and Phrases: quasilinear elliptic Dirichlet problems, asymptotic behaviour, singularity in the variable, quadratic nonlinearity in the gradient, integrability

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