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In this paper we obtain some results about a class of functions ̺ : Ω → R+, where Ω is an open set of R, which are related to the distance function from a fixed subset S̺ ⊂ ∂Ω. We deduce some imbedding theorems in weighted Sobolev spaces, where the weight function is a power of a function ̺.
with p ∈]1,+∞[. Suppose that Ω verifies suitable regularity assumptions. If p ≥ n, ai j ∈ L∞(Ω) (i, j = 1, . . . ,n), and the coefficients ai (i= 1, . . . ,n), a satisfy certain local summability conditions (with a > 0), then it is possible to obtain a uniqueness result for the problem (D) using a classical result of Alexandrov and Pucci (see  for the… (More)
In this paper we prove some interpolation inequalities between functions and their derivatives in the class of weighted Sobolev spaces defined on unbounded open subset Ω ⊂ Rn .
and Applied Analysis 3 In literature, several authors have considered different kinds of weighted spaces of Morrey type and their applications to the study of elliptic equations, both in the degenerate case and in the nondegenerate one see e.g., 9–11 . In this paper, given a weight ρ in a class of measurable functions G Ω see § 6 for its definition , we… (More)
In this paper we prove some a priori bounds for the solutions of the Dirichlet problem for elliptic equations with singular coefficients in weighted Sobolev spaces. Mathematics subject classification (2010): 35J25, 35B45, 35R05.
In this paper we study certain weighted Sobolev spaces defined on an open subset Ω of Rn (not necessarily bounded or regular) when the weight is a function related to the distance from a subset of ∂Ω . As an application, we prove boundedness and compactness results for operators in such weighted Sobolev spaces. c ⃝ 2012 Elsevier Inc. All rights reserved.