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.
On some results in weighted spaces under Chicco type conditions
CANALE, Anna
2006
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
