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

Marcello Lucia; Michael J. Puls

Analysis and Geometry in Metric Spaces (2015)

  • Volume: 3, Issue: 1, page 12 p., electronic only-12 p., electronic only
  • ISSN: 2299-3274

Abstract

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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.

How to cite

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Marcello Lucia, and Michael J. Puls. "The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces." Analysis and Geometry in Metric Spaces 3.1 (2015): 12 p., electronic only-12 p., electronic only. <http://eudml.org/doc/270810>.

@article{MarcelloLucia2015,
abstract = {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.},
author = {Marcello Lucia, Michael J. Puls},
journal = {Analysis and Geometry in Metric Spaces},
keywords = {Dirichlet problem at infinity; metric measure space; p-harmonic function; p-parabolic; p-Royden algebra; p-weak upper gradient; (p, p)-Sobolev inequality; -harmonic function},
language = {eng},
number = {1},
pages = {12 p., electronic only-12 p., electronic only},
title = {The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces},
url = {http://eudml.org/doc/270810},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Marcello Lucia
AU - Michael J. Puls
TI - The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces
JO - Analysis and Geometry in Metric Spaces
PY - 2015
VL - 3
IS - 1
SP - 12 p., electronic only
EP - 12 p., electronic only
AB - 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.
LA - eng
KW - Dirichlet problem at infinity; metric measure space; p-harmonic function; p-parabolic; p-Royden algebra; p-weak upper gradient; (p, p)-Sobolev inequality; -harmonic function
UR - http://eudml.org/doc/270810
ER -

References

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  10. [10] L. Sario and M. Nakai. Classification theory of Riemann surfaces. Die Grundlehren der mathematischen Wissenschaften, Band 164. Springer-Verlag, New York, 1970.  Zbl0199.40603
  11. [11] Nageswari Shanmugalingam. Newtonian spaces: an extension of Sobolev spaces to metric measure spaces. Rev. Mat. Iberoamericana, 16(2):243–279, 2000.  Zbl0974.46038
  12. [12] Nageswari Shanmugalingam. Some convergence results for p-harmonic functions on metric measure spaces. Proc. London Math. Soc. (3), 87(1):226–246, 2003.  Zbl1034.31006
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