Displaying similar documents to “Solvability of the Poisson equation in weighted Sobolev spaces”

Existence of solutions to the Poisson equation in L₂-weighted spaces

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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We consider the Poisson equation with the Dirichlet and the Neumann boundary conditions in weighted Sobolev spaces. The weight is a positive power of the distance to a distinguished plane. We prove the existence of solutions in a suitably defined weighted space.

On imbedding theorems for weighted anisotropic Sobolev spaces

Wojciech M. Zajączkowski (2002)

Applicationes Mathematicae

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Using the Il'in integral representation of functions, imbedding theorems for weighted anisotropic Sobolev spaces in 𝔼ⁿ are proved. By the weight we assume a power function of the distance from an (n-2)-dimensional subspace passing through the domain considered.

General Gagliardo Inequality and Applications to Weighted Sobolev Spaces

Antonio Avantaggiati, Paola Loreti (2009)

Bollettino dell'Unione Matematica Italiana

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In this paper we obtain a more general inequality with respect to a well known inequality due to Gagliardo (see [4], [5]). The inequality contained in [4], [5] has been extended to weighted spaces, obtained as cartesian product of measurable spaces. As application, we obtain a first order weighted Sobolev inequality. This generalize a previous result obtained in [2].

A quantitative approach to weighted Carleson condition

Israel P. Rivera-Ríos (2017)

Concrete Operators

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Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea [30, 31] for the operator [...] are obtained. As a consequence, some sufficient conditions for the boundedness of Min the two weight setting in the spirit of the results obtained by C. Pérez and E. Rela [26] and very recently by M. Lacey and S. Spencer [17] for the Hardy-Littlewood maximal operator are derived. As a byproduct some new quantitative estimates for the Poisson integral are obtained.

Solvability of the stationary Stokes system in spaces H ² - μ , μ ∈ (0,1)

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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We consider the stationary Stokes system with slip boundary conditions in a bounded domain. Assuming that data functions belong to weighted Sobolev spaces with weights equal to some power of the distance to some distinguished axis, we prove the existence of solutions to the problem in appropriate weighted Sobolev spaces.

Existence of solutions to the nonstationary Stokes system in H - μ 2 , 1 , μ ∈ (0,1), in a domain with a distinguished axis. Part 1. Existence near the axis in 2d

W. M. Zajączkowski (2007)

Applicationes Mathematicae

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We consider the nonstationary Stokes system with slip boundary conditions in a bounded domain which contains some distinguished axis. We assume that the data functions belong to weighted Sobolev spaces with the weight equal to some power function of the distance to the axis. The aim is to prove the existence of solutions in corresponding weighted Sobolev spaces. The proof is divided into three parts. In the first, the existence in 2d in weighted spaces near the axis is shown. In the...