| 1. |
- Adamowicz, Tomasz, et al.
(författare)
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The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(⋅)-harmonic measures
- 2016
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Ingår i: Annali di Matematica Pura ed Applicata. - : Springer. - 0373-3114 .- 1618-1891. ; 195:2, s. 623-658
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Tidskriftsartikel (refereegranskat)abstract
- We investigate various boundary decay estimates for p(⋅)-harmonic functions. For domains in Rn,n≥2satisfying the ball condition (C1,1-domains), we show the boundary Harnack inequality for p(⋅)-harmonic functions under the assumption that the variable exponent p is a bounded Lipschitz function. The proof involves barrier functions and chaining arguments. Moreover, we prove a Carleson-type estimate for p(⋅)-harmonic functions in NTA domains in Rn and provide lower and upper growth estimates and a doubling property for a p(⋅)-harmonic measure.
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| 2. |
- Aidanpää, Jan-Olov, et al.
(författare)
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Complex dynamic responses due to deviations of generator shape
- 2009
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Ingår i: 10th Conference on Dynamical Systems - Theory and Applications.
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Konferensbidrag (refereegranskat)abstract
- Earlier measurements in large synchronous generators indicate the existence of complex whirling motion, and also deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called Unbalanced Magnetic Pull (UMP). The target of this paper is to analyse responses due to certain deviations of shape in the rotor and the stator. In particular, the perturbation on the rotor is considered to be of oval character, and the perturbations of the stator are considered triangular and eccentric. It is concluded that harmful conditions can occur due to high amplitudes especially when the whirling of the rotor changes from forward to backward. During maintenance of hydro power generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complex whirling motion.
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| 3. |
- Aidanpää, Jan-Olov, et al.
(författare)
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Developments in rotor dynamical modeling of hydropower units
- 2009
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Ingår i: Proceedings of the IUTAM Symposium on Emerging Trends in Rotor Dynamics. - Dordrecht : Encyclopedia of Global Archaeology/Springer Verlag. - 9789400700192
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Konferensbidrag (refereegranskat)
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| 4. |
- Avelin, Benny, 1984-, et al.
(författare)
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Boundary estimates for solutions to operators of p-Laplace type with lower order terms
- 2011
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Ingår i: Journal of Differential Equations. - : Elsevier BV. - 0022-0396 .- 1090-2732. ; 250:1, s. 264-291
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we study the boundary behavior of solutions to equations of the form∇⋅A(x,∇u)+B(x,∇u)=0, in a domain Ω⊂Rn, assuming that Ω is a δ-Reifenberg flat domain for δ sufficiently small. The function A is assumed to be of p-Laplace character. Concerning B, we assume that |∇ηB(x,η)|⩽c|η|p−2, |B(x,η)|⩽c|η|p−1, for some constant c, and that B(x,η)=|η|p−1B(x,η/|η|), whenever x∈Rn, η∈Rn∖{0}. In particular, we generalize the results proved in J. Lewis et al. (2008) [12] concerning the equation ∇⋅A(x,∇u)=0, to equations including lower order terms.
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| 5. |
- Avelin, Benny, et al.
(författare)
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Optimal doubling, reifenberg flatness and operators of p-laplace type
- 2011
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Ingår i: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 74:17, s. 5943-5955
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider equations of p-Laplace type of the form ∇⋅A(x,∇u)=0. Concerning A we assume, for p∈(1,∞) fixed, an appropriate ellipticity type condition, Hölder continuity in x and that A(x,η)=|η|p−1A(x,η/|η|) whenever x∈Rn and η∈Rn∖{0}. Let Ω⊂Rn be a bounded domain, let D be a compact subset of Ω. We say that is the A-capacitary function for D in Ω if on D, on ∂Ω in the sense of and in Ω∖D in the weak sense. We extend to Rn∖Ω by putting on Rn∖Ω. Then there exists a unique finite positive Borel measure on Rn, with support in ∂Ω, such that In this paper, we prove that if Ω is Reifenberg flat with vanishing constant, then for every τ, 0<τ≤1. In particular, we prove that is an asymptotically optimal doubling measure on ∂Ω.
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| 6. |
- Grafström, Anton, et al.
(författare)
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Why well spread probability samples are balanced
- 2013
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Ingår i: Open Journal of Statistics. - : Scientific Research Publishing. - 2161-718X .- 2161-7198. ; 3:1, s. 36-41
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Tidskriftsartikel (refereegranskat)abstract
- When sampling from a finite population there is often auxiliary information available on unit level. Such information can be used to improve the estimation of the target parameter. We show that probability samples that are well spread in the auxiliary space are balanced, or approximately balanced, on the auxiliary variables. A consequence of this balancing effect is that the Horvitz-Thompson estimator will be a very good estimator for any target variable that can be well approximated by a Lipschitz continuous function of the auxiliary variables. Hence we give a theoretical motivation for use of well spread probability samples. Our conclusions imply that well spread samples, combined with the HorvitzThompson estimator, is a good strategy in a varsity of situations.
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| 7. |
- Lundström, Niklas L.P.
(författare)
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Bifurcations and Strange Attractors in a Climate Related System
- 2005
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Ingår i: Differentsial'nye Uravneniya i Protsessy Upravleniya / Differential Equations and Control Processes. - 1817-2172. ; :1, s. 1-53
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Tidskriftsartikel (refereegranskat)abstract
- R. V. Bekryaev derived a system for a horizontally baroclinic atmosphere consisting of six ordinary differential equations. We prove dissipativity and find estimates for the location of the global attractor. The evolution of a complicated attractor is analysed with a Poincar'e map showing difficult bifurcation behaviour. Investigations in bifurcation diagrams show a rich dynamical behaviour including a lot of known complicated bifurcations, of which a fold-Hopf bifurcation is examined in detail. Finally, we give some theory about the Lyapunov spectra and present a method for determining the exponents.
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| 8. |
- Lundström, Niklas L.P. 1980-, et al.
(författare)
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Decay of a p-harmonic measure in the plane
- 2013
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Ingår i: Annales Academiae Scientiarum Fennicae Mathematica. - : Suomalainen Tiedeakatemia. - 1239-629X .- 1798-2383. ; 38:1, s. 351-366
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Tidskriftsartikel (refereegranskat)abstract
- We study the asymptotic behaviour of a p-harmonic measure w(p), p is an element of (1, infinity], in a domain Omega subset of R-2, subject to certain regularity constraints. Our main result is that w(p) (B (w, delta) boolean AND partial derivative Omega, w(0)) approximate to delta(q) as delta -> 0(+), where q = q(v,p) is given explicitly as a function of v and p. Here, v is related to properties of Omega near w. If p = infinity, this extends to some domains in R-n. By a result due to Hirata, our result implies that the p-Green function for p is an element of (1, 2) is not quasi-symmetric in plane C-1,C-1-domains.
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| 9. |
- Lundström, Niklas L.P., et al.
(författare)
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Dynamics in large generators due to oval rotorand triangular stator shape
- 2011
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Ingår i: Acta Mechanica Sinica. - Beijing : Science Press. - 0567-7718 .- 0459-1879 .- 1614-3116. ; 27:1, s. 18-27
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Tidskriftsartikel (refereegranskat)abstract
- Earlier measurements in large synchronous generatorsindicate the existence of complex whirling motion,and also deviations of shape in both the rotor and the stator.These non-symmetric geometries produce an attraction forcebetween the rotor and the stator, called unbalanced magneticpull (UMP). The target of this paper is to analyse responsesdue to certain deviations of shape in the rotor and the stator.In particular, the perturbation on the rotor is consideredto be of oval character, and the perturbations of the statorare considered triangular. By numerical and analytical methodsit is concluded for which generator parameters harmfulconditions, such as complicated whirling motion and highamplitudes, will occur. During maintenance of hydro powergenerators the shapes of the rotor and stator are frequentlymeasured. The results from this paper can be used to evaluatesuch measurements and to explain the existence of complexwhirling motion.
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| 10. |
- Lundström, Niklas L P, 1980-
(författare)
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Estimates for p-harmonic functions vanishing on a flat
- 2011
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Ingår i: Nonlinear Analysis. - : Elsevier. - 0362-546X .- 1873-5215. ; 74:18, s. 6852-6860
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Tidskriftsartikel (refereegranskat)abstract
- We study p-harmonic functions in a domain ΩCRn near an m-dimensional plane (an m-flat) Λm, where 0≤m≤n−1. In particular, let u be a positive p-harmonic function, with n<p≤∞, vanishing on a portion of Λm, and suppose that β=(p−n+m)/(p−1), with β=1 if p=∞. We prove, using certain barrier functions, that u ≈ d (x.Λm)8 near Λm.The lower bound holds also in the range n−m<p≤∞. Moreover, u∈C0,β near Λm and β is the optimal Hölder exponent of u.
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