IJPAM: Volume 13, No. 2 (2004)

QUASILINEAR EQUATIONS WITH
DISCONTINUOUS COEFFICIENTS

Maria Alessandra Ragusa
Department of Mathematics and Informatics
University of Catania
Viale Andrea Doria 6, 95125 Catania, ITALY
e-mail: maragusa@dmi.unict.it


Abstract.In the paper the author, using Aleksandrov-Pucci maximum principle, proves an $L^\infty$ a priori estimate and also uniqueness for weak solution $u$ of a Dirichlet problem associated to quasilinear strictly elliptic equations with Charatheodory coefficients. The results obtained are a first step in the study of weak solvability of boundary value problems for quasilinear elliptic equations.

Received: March 4, 2004

AMS Subject Classification: 31B10, 43A15, 35K20, 32A37, 46E35

Key Words and Phrases: quasilinear operator, divergence form equations, uniqueness of solution of Dirichlet problem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 2