Hölder continuity for Trudinger's equation in measure spaces

Details Hölder continuity for Trudinger's equation in measure spaces Hölder continuity for Trudinger's equation in measure spaces

2011-03-09

arxiv.org/abs/1103.1845v1

Calc. Var. Partial Differential Equations, 2011

Mathematics

Analysis of PDEs

36 pages

Scientific paper

We complete the study of the regularity for Trudinger's equation by proving
that weak solutions are H\"older continuous also in the singular case. The
setting is that of a measure space with a doubling non-trivial Borel measure
supporting a Poincar\'e inequality. The proof uses the Harnack inequality and
intrinsic scaling.

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