Harnack inequality for parabolic quasi minimizers on metric spaces

  • Andreas Herán

    Universität Erlangen-Nürnberg, Germany
Harnack inequality for parabolic quasi minimizers on metric spaces cover

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Abstract

We are concerned with local parabolic quasi-minimizers on metric measure spaces. The measure space is assumed to fulfill a doubling and an annular-decay property and to support a weak (1, )-Poincaré inequality, while is associated to a Carathéodory integrand obeying -growth assumptions for . We are able to show a parabolic Harnack inequality under these assumptions. The quadratic case has already been considered in [25], whereas the superquadratic case, at least to our knowledge, has not even been treated in the euclidean setting. The proof following the ideas of DiBenedetto, Gianazza and Vespri in [9].

Cite this article

Andreas Herán, Harnack inequality for parabolic quasi minimizers on metric spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 3, pp. 565–592

DOI 10.4171/RLM/905