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1
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The Dirichlet problem in weighted spaces on a dihedral domain

100%
Kubica A.
Banach Center Publications
|
2009
|
tom 86
|
nr 1
207-222
EN
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.
2
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The regularity of weak and very weak solutions of the Poisson equation on polygonal domains with mixed boundary conditions (part I)

100%
Kubica A.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 4
443-456
EN
We examine the regularity of weak and very weak solutions of the Poisson equation on polygonal domains with data in L². We consider mixed Dirichlet, Neumann and Robin boundary conditions. We also describe the singular part of weak and very weak solutions.
3
Content available remote

The regularity of weak and very weak solutions of the Poisson equation on polygonal domains with mixed boundary conditions (part II)

100%
Kubica A.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 1
17-36
EN
We examine the regularity of weak and very weak solutions of the Poisson equation on polygonal domains with data in L². We consider mixed Dirichlet, Neumann and Robin boundary conditions. We also describe the singular part of weak and very weak solutions.
4
Content available remote

A parabolic system in a weighted Sobolev space

64%
Kubica A., Zajączkowski W.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 2
169-191
EN
We examine the regularity of solutions of a certain parabolic system in the weighted Sobolev space $W^{2,1}_{2,μ}$, where the weight is of the form $r^{μ}$, r is the distance from a distinguished axis and μ ∈ (0,1).
5
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A priori estimates in weighted spaces for solutions of the Poisson and heat equations

64%
Kubica A., Zajączkowski W.
Applicationes Mathematicae
|
2007
|
tom 34
|
nr 4
431-444
EN
We prove a priori estimates for solutions of the Poisson and heat equations in weighted spaces of Kondrat'ev type. The weight is a power of the distance from a distinguished axis.
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