Displaying similar documents to “Some remarks on a class of weight functions”

Weighted Miranda-Talenti inequality and applications to equations with discontinuous coefficients

Salvatore Leonardi (2002)

Commentationes Mathematicae Universitatis Carolinae

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Let Ω be an open bounded set in ℝ n ( n ≥ 2 ) , with C 2 boundary, and N p , λ ( Ω ) ( 1 < p < + ∞ , 0 ≤ λ < n ) be a weighted Morrey space. In this note we prove a weighted version of the Miranda-Talenti inequality and we exploit it to show that, under a suitable condition of Cordes type, the Dirichlet problem: ∑ i , j = 1 n a i j ( x ) ∂ 2 u ∂ x i ∂ x j = f ( x ) ∈ N p , λ ( Ω ) in Ω u = 0 on ∂ Ω has a unique strong solution in the functional space u ∈ W 2 , p ∩ W o 1 , p ( Ω ) : ∂ 2 u ∂ x i ∂ x j ∈ N p , λ ( Ω ) , i , j = 1 , 2 , ... , n .

Some notes on embedding for anisotropic Sobolev spaces

Hongliang Li, Quinxiu Sun (2011)

Czechoslovak Mathematical Journal

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In this paper, we prove new embedding theorems for generalized anisotropic Sobolev spaces, W Λ p , q ( w ) r 1 , ⋯ , r n and W X r 1 , ⋯ , r n , where Λ p , q ( w ) is the weighted Lorentz space and X is a rearrangement invariant space in ℝ n . The main methods used in the paper are based on some estimates of nonincreasing rearrangements and the applications of B p weights.

Embeddings of doubling weighted Besov spaces

Dorothee D. Haroske, Philipp Skandera (2014)

Banach Center Publications

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We study continuous embeddings of Besov spaces of type B p , q s ( ℝ ⁿ , w ) , where s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞, and the weight w is doubling. This approach generalises recent results about embeddings of Muckenhoupt weighted Besov spaces. Our main argument relies on appropriate atomic decomposition techniques of such weighted spaces; here we benefit from earlier results by Bownik. In addition, we discuss some other related weight classes briefly and compare corresponding results.

Existence of solutions to the (rot,div)-system in L p -weighted spaces

Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, v · n ̅ | S = 0 , S = ∂Ω in weighted L p -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.

Sharp embedding results for spaces of smooth functions with power weights

Martin Meyries, Mark Veraar (2012)

Studia Mathematica

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We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on ℝ d , equipped with power weights w ( x ) = | x | γ , γ > -d. We prove two-weight Sobolev embeddings for these spaces. Moreover, we precisely characterize for which parameters the embeddings hold. The proofs are presented in such a way that they also hold for vector-valued functions.