| 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. |
- 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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| 6. |
- 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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| 7. |
- Lundström, Niklas L. P., 1980-, et al.
(författare)
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Estimates of p-harmonic functions in planar sectors
- 2023
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Ingår i: Arkiv för matematik. - : International Press of Boston. - 0004-2080 .- 1871-2487. ; 61:1, s. 141-175
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Tidskriftsartikel (refereegranskat)abstract
- Suppose that p∈(1,∞], ν∈[1/2,∞), Sν= {(x1, x2)∈R2\{(0, 0)}:|φ|< π/2ν}, where φ is the polar angle of (x1, x2). Let R>0 and ωp(x) be the p-harmonic measure of ∂B(0,R)∩Sν at x with respect to B(0,R)∩Sν. We prove that there exists a constant C such that whenever x∈B(0,R)∩S2ν and where the exponent k(ν, p) is given explicitly as a function of ν and p. Using this estimate we derive local growth estimates for p-sub- and p-superharmonic functions in planar domains which are locally approximable by sectors, e.g., we conclude bounds of the rate of convergence near the boundary where the domain has an inwardly or outwardly pointed cusp. Using the estimates of p-harmonic measure we also derive a sharp Phragmén-Lindelöf theorem for p-subharmonic functions in the unbounded sector Sν. Moreover, if p=∞ then the above mentioned estimates extend from the setting of two-dimensional sectors to cones in Rn. Finally, when ν∈(1/2,∞) and p∈(1,∞) we prove uniqueness (modulo normalization) of positive p-harmonic functions in Sν vanishing on ∂Sν.
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| 8. |
- Lundström, Niklas L. P., 1980-
(författare)
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Growth of subsolutions to fully nonlinear equations in halfspaces
- 2022
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Ingår i: Journal of Differential Equations. - : Academic Press. - 0022-0396 .- 1090-2732. ; 320, s. 143-173
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Tidskriftsartikel (refereegranskat)abstract
- We characterize lower growth estimates for subsolutions in halfspaces of fully nonlinear partial differential equations on the form F(x,u,Du,D2u)=0 in terms of solutions to ordinary differential equations built upon assumptions on F. Using this characterization we derive several sharp Phragmen–Lindelöf-type theorems for certain classes of well known PDEs. The equation need not be uniformly elliptic nor homogeneous and we obtain results both in case the subsolution is bounded or unbounded. Among our results we retrieve classical estimates in the halfspace for p-subharmonic functions and extend those to more general equations; we prove sharp growth estimates, in terms of k and the asymptotic behavior of ∫0RC(s)ds, for subsolutions of equations allowing for sublinear growth in the gradient of the form C(|x|)|Du|k with k≥1; we establish a Phragmen–Lindelöf theorem for weak subsolutions of the variable exponent p-Laplace equation in halfspaces, 11, of which we conclude sharpness by finding the "slowest growing" p(x)-harmonic function together with its corresponding family of p(x)-exponents. The paper ends with a discussion of our results from the point of view of a spatially dependent diffusion problem.
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| 9. |
- Lundström, Niklas L. P., 1980-
(författare)
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How to find simple nonlocal stability and resilience measures
- 2018
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Ingår i: Nonlinear dynamics. - : Springer. - 0924-090X .- 1573-269X. ; 93:2, s. 887-908
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Tidskriftsartikel (refereegranskat)abstract
- Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena cannot be traced by the widespread local stability and resilience measures, based on linearizations, accounting only for arbitrary small perturbations. Using numerical estimates of the size and shape of the basin of attraction, as well as the systems returntime to the attractor after given a perturbation, we construct simple nonlocal stability and resilience measures that record a systems ability to tackle both large and small perturbations. We demonstrate our approach on the Solow-Swan model of economic growth, an electro-mechanical system, a stage-structured population model as well as on a high-dimensional system, and conclude that the suggested measures detect dynamic behavior, crucial for a systems stability and resilience, which can be completely missed by local measures. The presented measures are also easy to implement on a standard laptop computer. We believe that our approach will constitute an important step toward filling a current gap in the literature by putting forward and explaining simple ideas and methods, and by delivering explicit constructions of several promising nonlocal stability and resilience measures.
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| 10. |
- Lundström, Niklas L. P., 1980-, et al.
(författare)
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Meeting yield and conservation objectives by harvesting both juveniles and adults
- 2019
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Ingår i: American Naturalist. - : University of Chicago Press. - 0003-0147 .- 1537-5323. ; 193:3, s. 373-390
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Tidskriftsartikel (refereegranskat)abstract
- Sustainable yields that are at least 80% of the maximum sustainable yield are sometimes referred to as "pretty good yields" (PGY). The range of PGY harvesting strategies is generally broad and thus leaves room to account for additional objectives besides high yield. Here, we analyze stage-dependent harvesting strategies that realize PGY with conservation as a second objective. We show that (1) PGY harvesting strategies can give large conservation benefits and (2) equal harvesting rates of juveniles and adults is often a good strategy. These conclusions are based on trade-off curves between yield and four measures of conservation that form in two established population models, one age-structured model and one stage-structured model, when considering different harvesting rates of juveniles and adults. These conclusions hold for a broad range of parameter settings, although our investigation of robustness also reveals that (3) predictions of the age-structured model are more sensitive to variations in parameter values than those of the stage-structured model. Finally, we find that (4) measures of stability that are often quite difficult to assess in the field (e.g., basic reproduction ratio and resilience) are systematically negatively correlated with impacts on biomass and size structure, so that these later quantities can provide integrative signals to detect possible collapses.
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