| 1. |
- Aleman, A., et al.
(författare)
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On the decrease of kinetic energy with depth in wave–current interactions
- 2020
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 378:3-4, s. 853-872
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Tidskriftsartikel (refereegranskat)abstract
- We study wave–current interactions in two-dimensional water flows with constant vorticity over a flat bed. We establish decay rates for the velocity beneath spatially periodic surface waves without any restrictions on the wave amplitude. The approach relies on complex function theory and overcomes the intricacies inherent to nonlinear flow patterns by taking advantage of specific structural properties of the governing equations for water waves.
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| 2. |
- Andersson, Mats, 1957, et al.
(författare)
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Explicit representation of membership of polynomial ideals
- 2011
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 349:2, s. 345-365
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a new division formula on projective space which provides explicit solutions to various polynomial division problems with sharp degree estimates. We consider simple examples as the classical Macaulay theorem as well as a quite recent result by Hickel, related to the effective Nullstellensatz. We also obtain a related result that generalizes Max Noether's classical AF + BG theorem.
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| 3. |
- Andersson, Mats, 1957, et al.
(författare)
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Global representation of Segre numbers by Monge–Ampère products
- 2021
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 380:1-2, s. 349-391
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Tidskriftsartikel (refereegranskat)abstract
- On a reduced analytic space X we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding quotient B(X) that we think of as an analogue of the Chow group and a refinement of de Rham cohomology. This group allows us to study both global and local intersection theoretic properties. We provide many B-analogues of classical intersection theoretic constructions: For an analytic subspace V⊂ X we define a B-Segre class, which is an element of B(X) with support in V. It satisfies a global King formula and, in particular, its multiplicities at each point coincide with the Segre numbers of V. When V is cut out by a section of a vector bundle we interpret this class as a Monge–Ampère-type product. For regular embeddings we construct a B-analogue of the Gysin morphism.
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| 4. |
- Andersson, Mats, 1957, et al.
(författare)
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The ∂¯ -equation on a non-reduced analytic space
- 2019
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 374:1-2, s. 553-599
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Tidskriftsartikel (refereegranskat)abstract
- Let X be a, possibly non-reduced, analytic space of pure dimension. We introduce a notion of ∂¯ -equation on X and prove a Dolbeault–Grothendieck lemma. We obtain fine sheaves AXq of (0, q)-currents, so that the associated Dolbeault complex yields a resolution of the structure sheaf OX. Our construction is based on intrinsic semi-global Koppelman formulas on X.
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| 5. |
- Andersson, Mats, et al.
(författare)
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The (partial derivative)over-bar-equation on a non-reduced analytic space
- 2019
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 374:1-2, s. 553-599
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Tidskriftsartikel (refereegranskat)abstract
- Let X be a, possibly non-reduced, analytic space of pure dimension. We introduce a notion of -equation on X and prove a Dolbeault-Grothendieck lemma. We obtain fine sheaves AXq of (0,q)-currents, so that the associated Dolbeault complex yields a resolution of the structure sheaf OX. Our construction is based on intrinsic semi-global Koppelman formulas on X.
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| 6. |
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| 7. |
- Andreasson, Håkan, 1966, et al.
(författare)
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The formation of black holes in spherically symmetric gravitational collapse
- 2011
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Ingår i: MATHEMATISCHE ANNALEN. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 350:3, s. 683-705
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Tidskriftsartikel (refereegranskat)abstract
- We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of radially outgoing null geodesics where the area radius r along each geodesic is bounded by 2M, the timelike lines r=c [0,2M] are incomplete, and for r > 2M the metric converges asymptotically to the Schwarzschild metric with mass M. The initial data that we construct guarantee the formation of a black hole in the evolution. We give examples of such initial data with the additional property that the solutions exist for all r ≥ 0 and all Schwarzschild time, i. e., we obtain global existence in Schwarzschild coordinates in situations where the initial data are not small. Some of our results are also established for the Einstein equations coupled to a general matter model characterized by conditions on the matter quantities.
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| 8. |
- Arone, Gregory, 1966-, et al.
(författare)
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Suspension spectra of matrix algebras, the rank filtration, and rational noncommutative CW-spectra
- 2023
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 386:1-2, s. 35-84
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Tidskriftsartikel (refereegranskat)abstract
- In a companion paper (Arone et al. in Noncommutative CW-spectra as enriched presheaves on matrix algebras, arXiv:2101.09775, 2021) we introduced the stable ∞-category of noncommutative CW-spectra, which we denoted NSp. Let M denote the full spectrally enriched subcategory of NSp whose objects are the non-commutative suspension spectra of matrix algebras. In Arone et al. (2021) we proved that NSp is equivalent to the ∞-category of spectral presheaves on M. In this paper we investigate the structure of M, and derive some consequences regarding the structure of NSp. To begin with, we introduce a rank filtration of M. We show that the mapping spectra of M map naturally to the connective K-theory spectrum ku, and that the rank filtration of M is a lift of the classical rank filtration of ku. We describe the subquotients of the rank filtration in terms of spaces of direct-sum decompositions which also arose in the study of K-theory and of Weiss’s orthogonal calculus. We prove that the rank filtration stabilizes rationally after the first stage. Using this we give an explicit model of the rationalization of NSp as presheaves of rational spectra on the category of finite-dimensional Hilbert spaces and unitary transformations up to scaling. Our results also have consequences for the p-localization and the chromatic localization of M.
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| 9. |
- Avelin, Benny
(författare)
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On time dependent domains for the degenerate p-parabolic equation : Carleson estimate and Holder continuity
- 2016
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Ingår i: Mathematische Annalen. - : Springer Science and Business Media LLC. - 0025-5831 .- 1432-1807. ; 364:1-2, s. 667-686
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we propose a definition of "parabolic NTA" for solutions to the degenerate p-parabolic equation. Given this definition we prove the Carleson estimate, originally proved for this equation in Avelin et al. (J Eur Math Soc, 2015) for cylindrical domains. Moreover we study a non-optimal, stronger "outer corkscrew" condition, such that we obtain Holder continuity up to the boundary, for non-negative solutions vanishing on a part of the boundary.
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| 10. |
- Balci, Anna Kh., et al.
(författare)
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A pointwise differential inequality and second-order regularity for nonlinear elliptic systems
- 2022
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Ingår i: Mathematische Annalen. - : Springer Berlin/Heidelberg. - 0025-5831 .- 1432-1807. ; 383:3-4, s. 1775-1824
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Tidskriftsartikel (refereegranskat)abstract
- A sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic systems in domains in R-n are derived. Both local and global estimates are established. Minimal assumptions on the boundary of the domain are required for the latter. In the special case of the p-Laplace system, our conclusions broaden the range of the admissible values of the exponent p previously known.
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