Nonhomogeneous variational problems and quasi-minimizers on metric spaces

Jasun Gong*, Juan J. Manfredi, Mikko Parviainen

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

We show that quasi-minimizers of non-homogeneous energy functionals are locally Hölder continuous and satisfy the Harnack inequality on metric measure spaces. We assume that the space is doubling and supports a Poincaré inequality. The proof is based on the De Giorgi method, combined with the expansion of positivity technique.

Original languageEnglish
Pages (from-to)247-271
Number of pages25
JournalManuscripta Mathematica
Volume137
Issue number1-2
DOIs
Publication statusPublished - Jan 2012
MoE publication typeA1 Journal article-refereed

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