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- Title
Regularity of quasi-minimizers on metric spaces.
- Authors
Kinnunen, Juha; Shanmugalingam, Nageswari
- Abstract
Using the theory of Sobolev spaces on a metric measure space we are able to apply calculus of variations and define p-harmonic functions as minimizers of the p-Dirichlet integral. More generally, we study regularity properties of quasi-minimizers of p-Dirichlet integrals in a metric measure space. Applying the De Giorgi method we show that quasi-minimizers, and in particular p-harmonic functions, satisfy Harnack's inequality, the strong maximum principle, and are locally Hölder continuous, if the space is doubling and supports a Poincaré inequality.
- Publication
Manuscripta Mathematica, 2001, Vol 105, Issue 3, p401
- ISSN
0025-2611
- Publication type
Article
- DOI
10.1007/s002290100193