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Träfflista för sökning "AMNE:(NATURVETENSKAP Matematik Matematisk analys) ;pers:(Björn Jana)"

Sökning: AMNE:(NATURVETENSKAP Matematik Matematisk analys) > Björn Jana

  • Resultat 1-10 av 53
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1.
  • Björn, Anders, 1966-, et al. (författare)
  • First-order Sobolev spaces on metric spaces
  • 2009
  • Ingår i: <em>Function Spaces, Inequalities and Interpolation</em> (Paseky, 2009). - Prague : Matfyzpress. - 9788073780852 ; , s. 1-29
  • Konferensbidrag (refereegranskat)
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2.
  • Aikawa, Hiroaki, et al. (författare)
  • Dichotomy of global capacity density in metric measure spaces
  • 2018
  • Ingår i: Advances in Calculus of Variations. - : WALTER DE GRUYTER GMBH. - 1864-8258 .- 1864-8266. ; 11:4, s. 387-404
  • Tidskriftsartikel (refereegranskat)abstract
    • The variational capacity cap(p) in Euclidean spaces is known to enjoy the density dichotomy at large scales, namely that for every E subset of R-n, infx is an element of R(n)cap(p)(E boolean AND B(x, r), B(x, 2r))/cap(p)(B(x, r), B(x, 2r)) is either zero or tends to 1 as r -amp;gt; infinity. We prove that this property still holds in unbounded complete geodesic metric spaces equipped with a doubling measure supporting a p-Poincare inequality, but that it can fail in nongeodesic metric spaces and also for the Sobolev capacity in R-n. It turns out that the shape of balls impacts the validity of the density dichotomy. Even in more general metric spaces, we construct families of sets, such as John domains, for which the density dichotomy holds. Our arguments include an exact formula for the variational capacity of superlevel sets for capacitary potentials and a quantitative approximation from inside of the variational capacity.
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3.
  • Björn, Anders, et al. (författare)
  • A uniqueness result for functions with zero fine gradient on quasiconnected and finely connected sets
  • 2020
  • Ingår i: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V. - Pisa, Italy : SCUOLA NORMALE SUPERIORE. - 0391-173X .- 2036-2145. ; 21, s. 293-301
  • Tidskriftsartikel (refereegranskat)abstract
    • We show that every Sobolev function in W-loc(1, p) (U) on a p-quasiopen set U subset of R-n with a.e.-vanishing p-fine gradient is a.e.-constant if and only if U is p-quasiconnected. To prove this we use the theory of Newtonian Sobolev spaces on metric measure spaces, and obtain the corresponding equivalence also for complete metric spaces equipped with a doubling measure supporting a p-Poincare inequality. On unweighted R-n, we also obtain the corresponding result for p-finely open sets in terms of p-fine connectedness, using a deep result by Latvala.
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4.
  • Björn, Anders, et al. (författare)
  • Boundary Regularity for the Porous Medium Equation
  • 2018
  • Ingår i: Archive for Rational Mechanics and Analysis. - : SPRINGER. - 0003-9527 .- 1432-0673. ; 230:2, s. 493-538
  • Tidskriftsartikel (refereegranskat)abstract
    • We study the boundary regularity of solutions to the porous medium equation in the degenerate range . In particular, we show that in cylinders the Dirichlet problem with positive continuous boundary data on the parabolic boundary has a solution which attains the boundary values, provided that the spatial domain satisfies the elliptic Wiener criterion. This condition is known to be optimal, and it is a consequence of our main theorem which establishes a barrier characterization of regular boundary points for general-not necessarily cylindrical-domains in . One of our fundamental tools is a new strict comparison principle between sub- and superparabolic functions, which makes it essential for us to study both nonstrict and strict Perron solutions to be able to develop a fruitful boundary regularity theory. Several other comparison principles and pasting lemmas are also obtained. In the process we obtain a rather complete picture of the relation between sub/superparabolic functions and weak sub/supersolutions.
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5.
  • Björn, Anders, et al. (författare)
  • Bounded Geometry andp-Harmonic Functions Under Uniformization and Hyperbolization
  • 2021
  • Ingår i: Journal of Geometric Analysis. - : SPRINGER. - 1050-6926 .- 1559-002X. ; 31, s. 5259-5308
  • Tidskriftsartikel (refereegranskat)abstract
    • The uniformization and hyperbolization transformations formulated by Bonk et al. in"Uniformizing Gromov Hyperbolic Spaces", Asterisque, vol 270 (2001), dealt with geometric properties of metric spaces. In this paper we consider metric measure spaces and construct a parallel transformation of measures under the uniformization and hyperbolization procedures. We show that if a locally compact roughly starlike Gromov hyperbolic space is equipped with a measure that is uniformly locally doubling and supports a uniformly localp-Poincare inequality, then the transformed measure is globally doubling and supports a globalp-Poincare inequality on the corresponding uniformized space. In the opposite direction, we show that such global properties on bounded locally compact uniform spaces yield similar uniformly local properties for the transformed measures on the corresponding hyperbolized spaces. We use the above results on uniformization of measures to characterize when a Gromov hyperbolic space, equipped with a uniformly locally doubling measure supporting a uniformly localp-Poincare inequality, carries nonconstant globally definedp-harmonic functions with finitep-energy. We also study some geometric properties of Gromov hyperbolic and uniform spaces. While the Cartesian product of two Gromov hyperbolic spaces need not be Gromov hyperbolic, we construct an indirect product of such spaces that does result in a Gromov hyperbolic space. This is done by first showing that the Cartesian product of two bounded uniform domains is a uniform domain.
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6.
  • Björn, Anders, 1966-, et al. (författare)
  • Classification of metric measure spaces and their ends using p-harmonic functions
  • 2022
  • Ingår i: Annales Fennici Mathematici. - : SUOMALAINEN TIEDEAKATEMIA. - 2737-0690 .- 2737-114X. ; 47:2, s. 1025-1052
  • Tidskriftsartikel (refereegranskat)abstract
    • By seeing whether a Liouville type theorem holds for positive, bounded, and/or finite p-energy p-harmonic and p-quasiharmonic functions, we classify proper metric spaces equipped with a locally doubling measure supporting a local p-Poincare inequality. Similar classifications have earlier been obtained for Riemann surfaces and Riemannian manifolds. We study the inclusions between these classes of metric measure spaces, and their relationship to the p-hyperbolicity of the metric space and its ends. In particular, we characterize spaces that carry nonconstant p-harmonic functions with finite p-energy as spaces having at least two well-separated p-hyperbolic sequences of sets towards infinity. We also show that every such space X has a function f is an element of/ LP(X) + R with finite p-energy.
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7.
  • Björn, Anders, et al. (författare)
  • Convergence and local-to-global results for p-superminimizers on quasiopen sets
  • 2023
  • Ingår i: Journal of Differential Equations. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0022-0396 .- 1090-2732. ; 365, s. 812-831
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, several convergence results for fine p-(super)minimizers on quasiopen sets in metric spaces are obtained. For this purpose, we deduce a Caccioppoli-type inequality and local-to-global principles for fine p-(super)minimizers on quasiopen sets. A substantial part of these considerations is to show that the functions belong to a suitable local fine Sobolev space. We prove our results for a complete metric space equipped with a doubling measure supporting a p-Poincare inequality with 1 < p < & INFIN;. However, most of & COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
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10.
  • Björn, Anders, et al. (författare)
  • Existence and almost uniqueness for p -harmonic Green functions on bounded domains in metric spaces
  • 2020
  • Ingår i: Journal of Differential Equations. - : ACADEMIC PRESS INC ELSEVIER SCIENCE. - 0022-0396 .- 1090-2732. ; 269:9, s. 6602-6640
  • Tidskriftsartikel (refereegranskat)abstract
    • We study (p -harmonic) singular functions, defined by means of upper gradients, in bounded domains in metric measure spaces. It is shown that singular functions exist if and only if the complement of the domain has positive capacity, and that they satisfy very precise capacitary identities for superlevel sets. Suitably normalized singular functions are called Green functions. Uniqueness of Green functions is largely an open problem beyond unweighted R n , but we show that all Green functions (in a given domain and with the same singularity) are comparable. As a consequence, for p -harmonic functions with a given pole we obtain a similar comparison result near the pole. Various characterizations of singular functions are also given. Our results hold in complete metric spaces with a doubling measure supporting a p-Poincar? inequality, or under similar local assumptions.
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  • Resultat 1-10 av 53

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