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On some L p -estimates for solutions of elliptic equations in unbounded domains

Sara MonsurròMaria Transirico — 2015

Mathematica Bohemica

In this review article we present an overview on some a priori estimates in L p , p > 1 , recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two L p -bounds, p > 2 , for the solution...

Some remarks on a class of weight functions

Loredana CasoMaria Transirico — 1996

Commentationes Mathematicae Universitatis Carolinae

In this paper we obtain some results about a class of functions ρ : Ω R + , where Ω is an open set of R n , which are related to the distance function from a fixed subset S ρ Ω . We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function ρ .

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