IJPAM: Volume 31, No. 2 (2006)

ON SOME RESULTS IN WEIGHTED SPACES
UNDER CHICCO TYPE CONDITIONS

A. Canale
Department of Mathematics and Informatics
Faculty of Science, MM.FF.NN.
University of Salerno
Via Ponte Don Melillo, Fisciano (Salerno), 84084, ITALY
e-mail: acanale@unisa.it


Abstract.In the present paper we consider weighted spaces where the weight is related to the distance function from a fixed subset $S$ of $\partial\Omega$.

In unbounded domains we study Dirichlet problem for linear elliptic equations in nondivergence form with discontinuous coefficients when the class of discontinuity is of Chicco type.

In particular we state some local and non local a priori bounds and study the dependence of the constants in the estimates. The coefficients of lower terms in the differential operator belong to weighted spaces and the principal coefficients are `near' to functions satisfying a condition of Chicco type. The conditions we impose on the coefficients allow us to apply embedding results to get local estimates.

Received: July 10, 2006

AMS Subject Classification: 35J25, 46E35

Key Words and Phrases: elliptic equations, embedding theorems, a priori bounds, weighted spaces, Chicco condition

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 31
Issue: 2