Nonhomogeneous Variational Problems and Quasi-Minimizers on Metric Spaces

Details Nonhomogeneous Variational Problems and Quasi-Minimizers on Metric Spaces Nonhomogeneous Variational Problems and Quasi-Minimizers on Metric Spaces

2010-08-30

arxiv.org/abs/1008.4976v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

We show that quasi-minimizers of non-homogeneous energy functionals on metric
measure spaces are locally H\"older continuous and satisfy the Harnack
inequality. We assume that the spaces are doubling and support a Poincar\'e
inequality. The proof is based on the De Giorgi method, combined with the
"expansion of positivity" technique.

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