On some results in weighted spaces under Cordes type conditions

Abstract

We study Dirichlet problem for linear elliptic equations in nondivergence form with discontinuous coefficients when the class of discontinuity is of Cordes type and domains are unbounded. In particular we state some local and non local a priori bounds in weighted spaces where the weight is related to the distance function from a fixed subset S of ¶­ 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 Cordes type. This condition allow us to apply embedding results near to a subset of ¶­ and for |x| large enough without further assumptions.

Keywords and phrases:

• Elliptic equations
• embedding theorems
• a priori bounds
• weighted spaces
• Cordes condition