| 1. |
- Abkar, A., et al.
(author)
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A Riesz representation formula for super-biharmonic functions
- 2001
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In: Annales Academiae Scientiarum Fennicae Mathematica. - 1239-629X .- 1798-2383. ; 26:2, s. 305-324
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Journal article (peer-reviewed)abstract
- Let u be a real-valued function defined on the unit disk D. We call u super-biharmonic provided that u is locally integrable and the bi-laplacian Delta (2)u is a positive distribution on D. In this paper, we shall establish a representation formula for super-biharmonic functions, This formula can be regarded as an analogue of the Poisson-Jensen representation formula for subharmonic functions.
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| 2. |
- Algervik, Robert, 1981-, et al.
(author)
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On Fournier-Gagliardo mixed norm spaces
- 2011
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In: Annales Academiae Scientiarum Fennicae Mathematica. - Helsinki : Finnish Academy of Science and Letters. - 1239-629X .- 1798-2383. ; 36, s. 493-508
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Journal article (peer-reviewed)abstract
- We study mixed norm spacesV (Rn)that arise in connection with embeddings ofSobolev spacesW11(Rn). We prove embeddings of V (Rn)into Lorentz type spaces defined in termsof iterative rearrangements. Basing on these results, we introduce the scale of mixed norm spacesVp(Rn). We prove that V ½ V p and we discuss some questions related to this embedding.
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| 3. |
- Avelin, Benny, 1984-
(author)
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On a one-phase free boundary problem
- 2013
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In: Annales Academiae Scientiarum Fennicae Mathematica. - : Finnish Academy of Science and Letters. - 1239-629X .- 1798-2383. ; 38:1, s. 181-191
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Journal article (other academic/artistic)abstract
- In this paper we extend a result regarding the free boundary regularity in a one-phaseproblem, by De Silva and Jerison [DJ], to non-divergence linear equations of second order.Roughly speaking we prove that the free boundary is given by a Lipschitz graph.
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| 4. |
- Baroni, Paolo, et al.
(author)
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Elliptic Interpolation Estimates for Non-Standard Growth Operators
- 2014
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In: Annales Academiae Scientiarum Fennicae Mathematica. - : Finnish Academy of Science and Letters. - 1239-629X .- 1798-2383. ; 39:1, s. 119-162
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Journal article (peer-reviewed)abstract
- We derive a class of potential estimates for elliptic equations with non-standard growth having a measure on the right-hand side; in particular our results allow to interpolate between the pointwise estimates available for solutions to this equation and the ones for the gradient. We allow bounded coefficients in BMO and VMO classes.
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| 5. |
- Bartolini, Gabriel, et al.
(author)
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ON THE CONNECTIVITY OF BRANCH LOCI OF MODULI SPACES
- 2013
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In: Annales Academiae Scientiarum Fennicae Mathematica. - : Academia Scientiarum Fennica. - 1239-629X .- 1798-2383. ; 38:1, s. 245-258
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Journal article (peer-reviewed)abstract
- The moduli space M-g of compact Riemann surfaces of genus g has orbifold structure and the set of singular points of the orbifold is the branch locus B-g. In this article we show that B-g is connected for genera three, four, thirteen, seventeen, nineteen and fiftynine, and disconnected for any other genus. In order to prove this we use Fuchsian groups, automorphisms of order 5 and 7 of Riemann surfaces, and calculations with GAP for some small genera.
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| 6. |
- Björn, Anders, et al.
(author)
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POWER-TYPE QUASIMINIMIZERS
- 2011
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In: ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA. - : Academia Scientiarum Fennica. - 1239-629X .- 1798-2383. ; 36:1, s. 301-319
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Journal article (peer-reviewed)abstract
- In this paper we examine the quasiminimizing properties of radial power-type functions u(x) = vertical bar x vertical bar(alpha) in R-n. We find the optimal quasiminimizing constant whenever u is a quasiminfinizer of the p-Dirichlet integral, p not equal n, and similar results when u is a quasisub- and quasisuperminimizer. We also obtain similar results for log-powers when p = n.
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| 7. |
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| 8. |
- Björn, Anders
(author)
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Removable singularities for H-p spaces of analytic functions, 0 < p < 1
- 2001
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In: Annales Academiae Scientiarum Fennicae Mathematica. - 1239-629X .- 1798-2383. ; 26:1, s. 155-174
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Journal article (peer-reviewed)abstract
- In this paper we study removable singularities for Hardy H-p spaces of analytic functions on general domains, mainly for 0 < p < 1. For each p < 1 we prove that there is a self-similar linear Canter set with Hausdorff dimension greater than 0.4p removable for H-p, thereby obtaining the first removable sets with positive Hausdorff dimension for 0 < p < 1. (Cf. the author's older result that a set E removable for H-P, 0 < p < 1, must satisfy dim E p.) We use this to extend some results earlier proved for 1 less than or equal to p < to 0 < p < infinity or 1/2 less than or equal to p < .
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| 9. |
- Björn, Anders, et al.
(author)
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SOBOLEV SPACES, FINE GRADIENTS AND QUASICONTINUITY ON QUASIOPEN SETS
- 2016
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In: Annales Academiae Scientiarum Fennicae Mathematica. - : SUOMALAINEN TIEDEAKATEMIA. - 1239-629X .- 1798-2383. ; 41:2, s. 551-560
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Journal article (peer-reviewed)abstract
- We study different definitions of Sobolev spaces on quasiopen sets in a complete metric space X equipped with a doubling measure supporting a p-Poincare inequality with 1 amp;lt; p amp;lt; infinity, and connect them to the Sobolev theory in R-n. In particular, we show that for quasiopen subsets of R-n the Newtonian functions, which are naturally defined in any metric space, coincide with the quasicontinuous representatives of the Sobolev functions studied by Kilpelainen and Maly in 1992.
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| 10. |
- Björn, Anders, et al.
(author)
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THE QUASISUPERMINIMIZING CONSTANT FOR THE MINIMUM OF TWO QUASISUPERMINIMIZERS IN R-n
- 2020
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In: Annales Academiae Scientiarum Fennicae Mathematica. - : SUOMALAINEN TIEDEAKATEMIA. - 1239-629X .- 1798-2383. ; 45, s. 215-225
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Journal article (peer-reviewed)abstract
- It was shown in Bjorn-Bjorn-Korte [5] that u := min{u(1), u(2)} is a (Q) over bar -quasisuper-minimizer if u(1) and u(2) are Q-quasisuperminimizers and (Q) over bar = 2Q(2)/(Q+1). Moreover, one-dimensional examples therein show that (Q) over bar is close to optimal. In this paper we give similar examples in higher dimensions. The case when u(1) and u(2) have different quasisuperminimizing constants is considered as well.
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