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

Existence of solutions vanishing near some axis for the nonstationary Stokes system with boundary slip conditions

W. M. Zajączkowski

Similarity:

We examine the nonstationary Stokes system in a bounded domain with the boundary slip conditions. We assume that there exists a line which crosses the domain and that the data belong to Sobolev spaces with weights equal to some powers of the distance to the line. Then the existence of solutions in Sobolev spaces with the corresponding weights is proved.

L²-data Dirichlet problem for weighted form Laplacians

Wojciech Kozłowski (2008)

Colloquium Mathematicae

Similarity:

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.

Global special regular solutions to the Navier-Stokes equations in axially symmetric domains under boundary slip conditions

Wojciech M. Zajączkowski

Similarity:

Existence and uniqueness of global regular special solutions to Navier-Stokes equations with boundary slip conditions in axially symmetric domains is proved. The proof of global existence relies on the global existence results for axially symmetric solutions which were obtained by Ladyzhenskaya and Yudovich-Ukhovskiĭ in 1968 who employed the problem for vorticity. In this paper the equations for vorticity also play a crucial role. Moreover, the boundary slip conditions imply appropriate...

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

Joanna Rencławowicz, Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

Similarity:

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.

The Dirichlet problem in weighted spaces on a dihedral domain

Adam Kubica (2009)

Banach Center Publications

Similarity:

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.

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

Similarity:

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...