Displaying similar documents to “Existence of solutions to the Poisson equation in L₂-weighted spaces”

Solvability of the Poisson equation in weighted Sobolev spaces

Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

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The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.

The Dirichlet problem in weighted spaces on a dihedral domain

Adam Kubica (2009)

Banach Center Publications

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We examine the Dirichlet problem for the Poisson equation and the heat equation in weighted spaces of Kondrat'ev's type on a dihedral domain. The weight is a power of the distance from a distinguished axis and it depends on the order of the derivative. We also prove a priori estimates.

L²-data Dirichlet problem for weighted form Laplacians

Wojciech Kozłowski (2008)

Colloquium Mathematicae

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We solve the L²-data Dirichlet boundary problem for a weighted form Laplacian in the unit Euclidean ball. The solution is given explicitly as a sum of four series.

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 heat equation in weighted Sobolev spaces

Wojciech M. Zajączkowski (2011)

Applicationes Mathematicae

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The existence of solutions to an initial-boundary value problem to the heat equation in a bounded domain in ℝ³ is proved. The domain contains an axis and the existence is proved in weighted anisotropic Sobolev spaces with weight equal to a negative power of the distance to the axis. Therefore we prove the existence of solutions which vanish sufficiently fast when approaching the axis. We restrict our considerations to the Dirichlet problem, but the Neumann and the third boundary value...

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].