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1
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Multipliers in Sobolev spaces and exact convergence rate estimates for the finite-difference schemes

100%
Jovanović B.
Banach Center Publications
|
1994
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tom 29
|
nr 1
165-173
EN
In this paper we present some recent results concerning convergence rate estimates for finite-difference schemes approximating boundary-value problems. Special attention is given to the problem of minimal smoothness of coefficients in partial differential equations necessary for obtaining the results.
2
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Traces of Besov, Triebel-Lizorkin and Sobolev Spaces on Metric Spaces

88%
Saksman E., Soto T.
Analysis and Geometry in Metric Spaces
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2017
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tom 5
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nr 1
98-115
EN
We establish trace theorems for function spaces defined on general Ahlfors regular metric spaces Z. The results cover the Triebel-Lizorkin spaces and the Besov spaces for smoothness indices s < 1, as well as the first order Hajłasz-Sobolev space M1,p(Z). They generalize the classical results from the Euclidean setting, since the traces of these function spaces onto any closed Ahlfors regular subset F ⊂ Z are Besov spaces defined intrinsically on F. Our method employs the definitions of the function spaces via hyperbolic fillings of the underlying metric space.
3
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Analysis and numerical approximation of a parabolic-hyperbolic transmission problem

75%
Jovanović B., Vulkov L.
Open Mathematics
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2012
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tom 10
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nr 1
73-84
EN
In this paper we investigate a mixed parabolic-hyperbolic initial boundary value problem in two disconnected intervals with Robin-Dirichlet conjugation conditions. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate is obtained.
4
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Holomorphic Sobolev spaces on the ball

65%
Beatrous F., Burbea J.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Introduction ..............................................................5 0. Preliminaries and notation....................................6 1. Hilbert spaces of holomorphic functions..............11 2. Some estimates ..................................................16 3. The space $L^p_q$............................................22 4. Norm estimates...................................................30 5. Sobolev norms....................................................35 6. Projections in Sobolev spaces............................47 References.............................................................56
5
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Linear extension operators for restrictions of function spaces to irregular open sets

63%
Rychkov V. S.
Studia Mathematica
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2000
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tom 140
|
nr 2
141-162
EN
Let an open set $Ω ⊂ ℝ^n$ satisfy for some 0≤d≤n and ε > 0 the condition: the $d$-Hausdorff content $H_d(Ω∩B) ≥ ε|B|^{d/n}$ for any ball B centered in Ω of volume |B|≤1. Let $H_p^s$ denote the Bessel potential space on $ℝ^n$ 1 < p < ∞,s > 0, and let $H_p^s[Ω]$ be the linear space of restrictions of elements of $H_p^s$ to Ω endowed with the quotient space norm. We find sufficient conditions for the existence of a linear extension operator for $H_p^s[Ω]$, i.e., a bounded linear operator $H_p^s[Ω]→H_p^s$ such that $ext⨍|_Ω}=⨍$ for all ⨍. The main result is that such an operator exists if (i) d > n-1 and s > (n-d)/min(p,2), or (ii) d≤n-1 and s-[s] > (n-d)/min(p,2). It is an open problem whether these assumptions are sharp.
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