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  • 1
    Electronic Resource
    Electronic Resource
    On strong solutions of Poisson's equation in Beppo Levi spaces (1992)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 43 (1992), S. 1023-1037 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung SciG ⊑ ℝ n (n ≥ 2) eine unbeschränkte offene Menge mit kompaktem Komplement und mit glattem Rand ∂G der KlasseC 2. InG betrachten wir das Randwertproblem — Δu=f,u¦∂g=Φ und beweisen die Existenz einer Lösungu εL 2,q(G) für beliebigef εL q(G) und Randwerte Φ εW 2-1/q,q(∂G) (1 〈q 〈 ∞). Dabei istL 2,q(G) der Raum aller Funktionenu εL Ioc q (G), die Distributionsableitungen zweiter Ordnung inL q (G) besitzen. Bezüglich der Eindeutigkeit solcher Lösungen zeigen wir, daß der entsprechende Nullraum die Dimensionn + 1 (n ≥ 2) besitzt.
    Notes: Abstract LetG ⊑ ℝsun (n ≥ 2) be an unbounded open set having a compact complement and a smooth boundary ∂G of classC 2. InG we consider the equations — Δu=f,u¦∂G=Φ and prove the existence of a solutionu εL 2,q(G) providedf εL q(G) and Φ εW 2 —1/q-q(∂G) (1 〈q 〈 ∞). HereL 2,q(G) is the space of all functionsu εL Ioc q (G) having all second order distributional derivatives inL q(G). Concerning the uniqueness of this solution we show that the corresponding nullspace has dimensionn + 1 (n ≥ 2).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00916426
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An initial-boundary-value problem for a certain density-dependent diffusion system (1987)
    Springer
    Mathematische Zeitschrift 194 (1987), S. 375-396 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01162244
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The Stokes-system in exterior domains:L p -estimates for small values of a resolvent parameter (1990)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 41 (1990), S. 829-842 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Wir betrachten das Resolventenproblem zum Stokes-System im Außenraum: $$- v \cdot \Delta u + \lambda \cdot u + \nabla \pi = f,divu = 0in\mathbb{R}^3 \backslash \bar \Omega ,$$ , Dabei ist Ω ein beschränktes Gebiet in ℝ3, mitC 2-Berandung ∂Ω. Ferner ist υε]0, ∞[ und λεℂ] −∞, 0]. Zusätzlich verlangen wir, daßu die Randbedingungu¦∂Ω=0 erfüllt. Lösungen (u,π) dieses Problems schätzen wir inL p -Normen ab, wobei vorausgesetzt wird, daß ¦λ¦ klein ist.
    Notes: Abstract We consider the resolvent problem for the Stokes-system in an exterior domain: $$- v \cdot \Delta u + \lambda \cdot u + \nabla \pi = f,divu = 0in\mathbb{R}^3 \backslash \bar \Omega ,$$ , with υε]0, ∞[, λεℂ] −∞, 0], Ω bounded domain in ℝ3, withC 2-boundary ∂Ω. In addition, Dirichlet boundary conditionsu¦∂Ω=0 are prescribed. Using the method of integral equations, we estimate solutions (u,π) inL p -norms, for small values of ¦λ¦.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945837
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Finite Element Methods for the Stokes System in Three-Dimensional Exterior Domains (1997)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 20 (1997), S. 245-269 
    Details
    ISSN: 0170-4214
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The article treats the question of how to numerically solve the Dirichlet problem for the Stokes system in the exterior of a three-dimensional bounded Lipschitz domain. In a first step, the solution of this problem is approximated by functions solving the Stokes system in a truncated domain and satisfying a suitable artificial boundary condition on the outer boundary of this truncated domain. In a second step, this new problem is approximately solved in finite element spaces related to a graded mesh as introduced by Goldstein [Math. Comp., 36, 387-404 (1981)]. The difference between this finite element approximation and the exact solution of the exterior Stokes problem is estimated in the norm of suitable unweighted L2-Sobolev spaces. These estimates are analogous to corresponding results which are known for the Poisson equation. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
    Type of Medium: Electronic Resource
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