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Tytuł artykułu

The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let p be a real number greater than one and let X be a locally compact, noncompact metric measure space that satisfies certain conditions. The p-Royden and p-harmonic boundaries of X are constructed by using the p-Royden algebra of functions on X and a Dirichlet type problem is solved for the p-Royden boundary. We also characterize the metric measure spaces whose p-harmonic boundary is empty.
Wydawca
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-01-23
zaakceptowano
2015-05-05
online
2015-06-01
Twórcy
  • Department of Mathematics, College of Staten Island-CUNY, 2800 Victory Boulevard, Staten Island, NY 10314, USA
  • Department of Mathematics, John Jay College-CUNY, 524 West 59th Street, New York, NY 10019, USA
Bibliografia
  • [1] Anders Björn and Jana Björn. Nonlinear potential theory onmetric spaces, volume17 ofEMS Tracts inMathematics. European Mathematical Society (EMS), Zürich, 2011.
  • [2] Moses Glasner and Richard Katz. The Royden boundary of a Riemannian manifold. Illinois J. Math., 14:488–495, 1970.
  • [3] Vladimir Gol0dshtein and Marc Troyanov. Axiomatic theory of Sobolev spaces. Expo. Math., 19(4):289–336, 2001.
  • [4] Daniel Hansevi. The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in Rn and metric spaces. arXiv: 1311.5955, 2013.
  • [5] Ilkka Holopainen, Urs Lang, and Aleksi Vähäkangas. Dirichlet problem at infinity on Gromov hyperbolic metric measure spaces. Math. Ann., 339(1):101–134, 2007. [WoS]
  • [6] Yong Hah Lee. Rough isometry and energy finite solutions of elliptic equations on Riemannian manifolds. Math. Ann., 318(1):181–204, 2000.
  • [7] Yong Hah Lee. Rough isometry and p-harmonic boundaries of complete Riemannianmanifolds. Potential Anal., 23(1):83–97, 2005.
  • [8] Michael J. Puls. Graphs of bounded degree and the p-harmonic boundary. Pacific J. Math., 248(2):429–452, 2010.
  • [9] H. L. Royden. On the ideal boundary of a Riemann surface. In Contributions to the theory of Riemann surfaces, Annals of Mathematics Studies, no. 30, pages 107–109. Princeton University Press, Princeton, N. J., 1953.
  • [10] L. Sario and M. Nakai. Classification theory of Riemann surfaces. Die Grundlehren der mathematischen Wissenschaften, Band 164. Springer-Verlag, New York, 1970.
  • [11] Nageswari Shanmugalingam. Newtonian spaces: an extension of Sobolev spaces to metric measure spaces. Rev. Mat. Iberoamericana, 16(2):243–279, 2000.
  • [12] Nageswari Shanmugalingam. Some convergence results for p-harmonic functions on metric measure spaces. Proc. London Math. Soc. (3), 87(1):226–246, 2003.
  • [13] Stephen Willard. General topology. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1970.
  • [14] Shing Tung Yau. Harmonic functions on complete Riemannian manifolds. Comm. Pure Appl. Math., 28:201–228, 1975.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_agms-2015-0008
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