| 1. |
- Aleksanyan, Hayk, 1987-
(författare)
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Regularity of boundary data in periodic homogenization of elliptic systems in layered media
- 2017
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Ingår i: Manuscripta mathematica. - : Springer-Verlag New York. - 0025-2611 .- 1432-1785. ; 154:1-2, s. 225-256
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Tidskriftsartikel (refereegranskat)abstract
- In this note we study periodic homogenization of Dirichlet problem for divergence type elliptic systems when both the coefficients and the boundary data are oscillating. One of the key difficulties here is the determination of the fixed boundary data corresponding to the limiting (homogenized) problem. This issue has been addressed in recent papers by Gérard-Varet and Masmoudi (Acta Math. 209:133–178, 2012), and by Prange (SIAM J. Math. Anal. 45(1):345–387, 2012), however, not much is known about the regularity of this fixed data. The main objective of this note is to initiate a study of this problem, and to prove several regularity results in this connection.
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| 2. |
- Aronsson, Gunnar
(författare)
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Construction of singular solutions to the p-harmonic equation and its limit equation for p=∞
- 1986
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Ingår i: Manuscripta mathematica. - 0025-2611 .- 1432-1785. ; 56:2, s. 135-158
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Tidskriftsartikel (refereegranskat)abstract
- Here, all solutions of the form u=rkf(φ) to the p-harmonic equation, div(|∇u|p-2∇u)=0, (p>2) in the plane are determined. One main result is a representation formula for such solutions. Further, solutions with an isolated singularity at the origin are constructed (Theorem 1). Graphical illustrations are given at the end of the paper. Finally, all solutions u=rkf(φ) of the limit equation for p=∞, ux2uxx+2uxuyuxy+uy2uyy=2, are constructed, some of which have a "strong" singularity at the origin (Theorem 2).
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| 3. |
- Aronsson, Gunnar
(författare)
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On certain singular solutions of the partial differential equation ux2uxx+2uxuyuxy+uy2uyy=0
- 1984
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Ingår i: Manuscripta mathematica. - 0025-2611 .- 1432-1785. ; 47:1-3, s. 133-151
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Tidskriftsartikel (refereegranskat)abstract
- The partial differential equation treated here is the formal limit of the p-harmonic equation in R2, for p →∞. Questions related to the smoothness of solutions and the possible existence of stationary points are central for the theory. The singular solutions constructed here bring new light on these questions.
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| 4. |
- Bergström, Jonas, et al.
(författare)
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On the cohomology of the Losev–Manin moduli space
- 2014
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Ingår i: Manuscripta mathematica. - : Springer Science and Business Media LLC. - 0025-2611 .- 1432-1785. ; 144:1, s. 241-252
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Tidskriftsartikel (refereegranskat)abstract
- We determine the cohomology of the Losev--Manin moduli space $\overline{M}_{0, 2 | n}$ of pointed genus zero curves as a representation of the product of symmetric groups $\Sg_2 \times \Sg_n$.
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| 5. |
- Besana, G. M., et al.
(författare)
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Peculiar loci of ample and spanned line bundles
- 2003
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Ingår i: Manuscripta mathematica. - : Springer Science and Business Media LLC. - 0025-2611 .- 1432-1785. ; 112:2, s. 197-219
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Tidskriftsartikel (refereegranskat)abstract
- The bad locus and the rude locus of an ample and base point free linear system on a smooth complex projective variety are introduced and studied. Polarized surfaces of small degree, or whose degree is the square of a prime, with nonempty bad loci are completely classified. Several explicit examples are offered to describe the variety of behaviors of the two loci.
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| 6. |
- Björn, Anders, et al.
(författare)
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Moser iteration for (quasi)minimizers on metric spaces
- 2006
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Ingår i: Manuscripta mathematica. - : Springer Science and Business Media LLC. - 0025-2611 .- 1432-1785. ; 121:3, s. 339-366
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Tidskriftsartikel (refereegranskat)abstract
- We study regularity properties of quasiminimizers of the p-Dirichlet integral on metric measure spaces. We adapt the Moser iteration technique to this setting and show that it can be applied without an underlying differential equation. However, we have been able to run the Moser iteration fully only for minimizers. We prove Caccioppoli inequalities and local boundedness properties for quasisub- and quasisuperminimizers. This is done in metric spaces equipped with a doubling measure and supporting a weak (1, p)-Poincaré inequality. The metric space is not required to be complete. We also provide an example which shows that the dilation constant from the weak Poincaré inequality is essential in the condition on the balls in the Harnack inequality. This fact seems to have been overlooked in the earlier literature on nonlinear potential theory on metric spaces.
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| 7. |
- Björn, Jana
(författare)
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Fine continuity on metric spaces
- 2008
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Ingår i: Manuscripta mathematica. - : Springer Science and Business Media LLC. - 0025-2611 .- 1432-1785. ; 125:3, s. 369-381
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Tidskriftsartikel (refereegranskat)abstract
- We obtain pointwise estimates for solutions of obstacle problems on metric measure spaces and prove that p-superharmonic functions are p-finely continuous. Consequently, we show that p-quasicontinuous functions are p-finely continuous at p-quasievery point. As a byproduct, we obtain the sufficiency part of the Wiener criterion in metric spaces without the assumption of linear local connectedness. © 2007 Springer-Verlag.
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| 8. |
- Bouw, Irene I., et al.
(författare)
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Dynamical Belyi maps and arboreal Galois groups
- 2021
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Ingår i: Manuscripta mathematica. - : Springer Science and Business Media LLC. - 0025-2611 .- 1432-1785. ; 165, s. 1-34
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Tidskriftsartikel (refereegranskat)abstract
- We consider a large class of so-called dynamical Belyi maps and study the Galois groups of iterates of such maps. From the combinatorial invariants of the maps, we construct a useful presentation of the geometric Galois groups as subgroups of automorphism groups of regular trees, in terms of iterated wreath products. Using results on the reduction of dynamical Belyi maps modulo certain primes, we obtain results on the corresponding arithmetic Galois groups of iterates. These lead to results on the behavior of the arithmetic Galois groups under specialization, with applications to dynamical sequences.
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| 9. |
- Coquand, Thierry, 1961, et al.
(författare)
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Generating non noetherian modules constructively
- 2004
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Ingår i: Manuscripta mathematica. - : Springer Science and Business Media LLC. - 0025-2611 .- 1432-1785. ; 115:4, s. 513-520
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Tidskriftsartikel (refereegranskat)abstract
- In [6], Heitmann gives a proof of a Basic Element Theorem, which has as corollaries some versions of the "Splitting-off" theorem of Serre and the Forster-Swan theorem in a non Noetherian setting. We give elementary and constructive proofs of such results. We introduce also a new notion of dimension for rings, which is only implicit in [6] and we present a generalisation of the Forster-Swan theorem, answering a question left open in [6].
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| 10. |
- Dahl, Mattias
(författare)
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Prescribing eigenvalues of the Dirac operator
- 2005
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Ingår i: Manuscripta mathematica. - : Springer Science and Business Media LLC. - 0025-2611 .- 1432-1785. ; 118:2, s. 191-199
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Tidskriftsartikel (refereegranskat)abstract
- In this note we show that every compact spin manifold of dimension <= 3 can be given a Riemannian metric for which a finite part of the spectrum of the Dirac operator consists of arbitrarily prescribed eigenvalues with multiplicity 1.
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