Local behavior of solutions of quasilinear parabolic equations on metric spaces

Published 21 Aug 2017 in math.AP | (1708.06329v1)

Abstract: We introduce a notion of quasilinear parabolic equations over metric measure spaces. Under sharp structural conditions, we prove that local weak solutions are locally bounded and satisfy the parabolic Harnack inequality. Applications include the parabolic maximum principle and pointwise estimates for weak solutions.

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Janna Lierl

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