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Moser iteration for (quasi)minimizers on metric spaces
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9677-8321
Helsinki University of Technology.
2006 (English)In: Manuscripta mathematica, ISSN 0025-2611, Vol. 121, no 3, 339-366 p.Article in journal (Refereed) Published
Abstract [en]

We study regularity properties of quasiminimizers of the p-Dirichlet integral on metric measure spaces. We adapt the Moser iteration technique to this setting and show that it can be applied without an underlying differential equation. However, we have been able to run the Moser iteration fully only for minimizers. We prove Caccioppoli inequalities and local boundedness properties for quasisub- and quasisuperminimizers. This is done in metric spaces equipped with a doubling measure and supporting a weak (1, p)-Poincaré inequality. The metric space is not required to be complete. We also provide an example which shows that the dilation constant from the weak Poincaré inequality is essential in the condition on the balls in the Harnack inequality. This fact seems to have been overlooked in the earlier literature on nonlinear potential theory on metric spaces.

Place, publisher, year, edition, pages
2006. Vol. 121, no 3, 339-366 p.
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URN: urn:nbn:se:liu:diva-18248DOI: 10.1007/s00229-006-0040-8OAI: diva2:217353
The original publication is available at Anders Björn and Niko Marola, Moser iteration for (quasi)minimizers on metric spaces, 2006, Manuscripta mathematica, (121), 3, 339-366. Copyright: Springer Science Business Media Available from: 2009-05-14 Created: 2009-05-14 Last updated: 2013-12-17Bibliographically approved

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