Loredana Caso

Some Remarks on Spaces of Morrey Type

We deepen the study of some Morrey type spaces, denoted by Mp,λ(Ω), defined on an unbounded open subset Ω of ℝn. In particular, we construct decompositions for functions belonging to two different subspaces of Mp,λ(Ω), which allow us to prove a compactness result for an operator in Sobolev spaces. We also introduce a weighted Morrey type space, settled between the above-mentioned subspaces.

Full length article: Weighted spaces and weighted norm inequalities on irregular domains

In this paper we study certain weighted Sobolev spaces defined on an open subset @W of R^n (not necessarily bounded or regular) when the weight is a function related to the distance from a subset of @?@W. As an application, we prove boundedness and compactness results for operators in such weighted Sobolev spaces.

Bounds for elliptic operators in weighted spaces

Some estimates for solutions of the Dirichlet problem for second-order elliptic equations are obtained in this paper. Here the leading coefficients are locally VMO functions, while the hypotheses on the other coefficients and the boundary conditions involve a suitable weight function.

Uniqueness results for elliptic problems with singular data

We obtain some uniqueness results for the Dirichlet problem for second-order elliptic equations in an unbounded open set without the cone property, and with data depending on appropriate weight functions. The leading coefficients of the elliptic operator are VMO functions. The hypotheses on the other coefficients involve the weight function.

Some uniqueness results for singular elliptic problems

We prove some uniqueness results for Dirichlet problems for second-order linear elliptic partial differential equations in non-divergence form with singular data in suitable weighted Sobolev spaces, on an open subset Ω of ℝn, n ≥ 2, not necessarily bounded or regular.

On the maximum principle for elliptic operators in weighted spaces

We establish a maximum principle for subsolutions of second order elliptic equations. In particular, we consider some linear operators with leading coefficients locally VMO, while the other coefficients and the boundary conditions involve a suitable weight function.MSC:35J25, 35R05, 35B50.

Uniqueness Results for Higher Order Elliptic Equations in Weighted Sobolev Spaces

We prove some uniqueness results for the solution of two kinds of Dirichlet boundary value problems for second- and fourth-order linear elliptic differential equations with discontinuous coefficients in polyhedral angles, in weighted Sobolev spaces.

Solvability of the Dirichlet Problem for Elliptic Equations with Singular Data

We give an overview on some results concerning the unique solvability of the Dirichlet problem in , , for second-order linear elliptic partial differential equations in nondivergence form and with singular data in weighted Sobolev spaces. We also extend such results to the planar case.