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 \partial\Omega 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 \partial\Omega and for |x| large enough without further assumptions.
On some results in weighted spaces under Cordes type conditions
CANALE, Anna
2007
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 \partial\Omega 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 \partial\Omega and for |x| large enough without further assumptions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
