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arXiv · 1008.4976

Nonhomogeneous Variational Problems and Quasi-Minimizers on Metric Spaces

Jasun Gong·Juan J. Manfredi·Mikko Parviainen
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Abstract

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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Jasun Gong, Juan J. Manfredi, Mikko Parviainen. 2010-08-30. Nonhomogeneous Variational Problems and Quasi-Minimizers on Metric Spaces. https://arxiv.org/abs/1008.4976

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