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arXiv · 2010.05727

Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic $p$-Laplace equation

Agnid Banerjee·Prashanta Garain·Juha Kinnunen
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Abstract

We establish a local boundedness estimate for weak subsolutions to a doubly nonlinear parabolic fractional $p$-Laplace equation. Our argument relies on energy estimates and a parabolic nonlocal version of De Giorgi's method. Furthermore, by means of a new algebraic inequality, we show that positive weak supersolutions satisfy a reverse H\"older inequality. Finally, we also prove a logarithmic decay estimate for positive supersolutions.

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Agnid Banerjee, Prashanta Garain, Juha Kinnunen. 2020-10-12. Some local properties of subsolutons and supersolutions for a doubly nonlinear nonlocal parabolic $p$-Laplace equation. https://arxiv.org/abs/2010.05727

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