IJPAM: Volume 31, No. 2 (2006)
UNDER CHICCO TYPE CONDITIONS
Department of Mathematics and Informatics
Faculty of Science, MM.FF.NN.
University of Salerno
Via Ponte Don Melillo, Fisciano (Salerno), 84084, ITALY
Abstract.In the present paper we consider weighted spaces where the weight is related to the distance function from a fixed subset of .
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
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