Self-improving phenomena in the calculus of variations on metric spaces
Doctoral thesis (article-based)
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AbstractThis 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.
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
- [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.