Self-improving phenomena in the calculus of variations on metric spaces

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Doctoral thesis (article-based)
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Date
2008
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Mcode
Degree programme
Language
en
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Verkkokirja (259 KB, 22 s.)
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Abstract
This dissertation studies the integrability properties of functions related to the calculus of variations on metric measure spaces that support a weak Poincaré inequality and a doubling measure. The work consists of three articles in which we study the higher integrability of functions satisfying a reverse Hölder inequality, quasiminimizers of the Dirichlet integral and superharmonic functions.
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Keywords
BMO function, Caccioppoli inequality, capacity, doubling measure, Gehring lemma, geodesic space, global integrability, higher integrability, Hölder domain, metric space, Muckenhoupt weight, Newtonian space, p-fatness, Poincaré inequality, quasiminimizer, reverse Hölder inequality, superharmonic function, superminimizer, stability
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Parts
  • [Publication 1]: Outi Elina Maasalo. The Gehring lemma in metric spaces. http://arxiv.org, arXiv:0704.3916v3 [math.CA]. © 2008 by author.
  • [Publication 2]: Outi Elina Maasalo and Anna Zatorska-Goldstein. Stability of quasiminimizers of the p-Dirichlet integral with varying p on metric spaces. Journal of the London Mathematical Society, to appear.
  • [Publication 3]: Outi Elina Maasalo. Global integrability of p-superharmonic functions on metric spaces. Journal d'Analyse Mathématique, to appear.
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