Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications

Shigeaki Koike; Andrzej Swiech; Shota Tateyama

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arXiv · 1811.07510

Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications

Shigeaki Koike·Andrzej Swiech·Shota Tateyama

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Abstract

The weak Harnack inequality for $L^p$-viscosity supersolutions of fully nonlinear second-order uniformly parabolic partial differential equations with unbounded coefficients and inhomogeneous terms is proved. It is shown that Hölder continuity of $L^p$-viscosity solutions is derived from the weak Harnack inequality for $L^p$-viscosity supersolutions. The local maximum principle for $L^p$-viscosity subsolutions and the Harnack inequality for $L^p$-viscosity solutions are also obtained. Several further remarks are presented when equations have superlinear growth in the first space derivatives.

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BibTeX RIS

Shigeaki Koike, Andrzej Swiech, Shota Tateyama. 2019-03-31. Weak Harnack inequality for fully nonlinear uniformly parabolic equations with unbounded ingredients and applications. https://arxiv.org/abs/1811.07510

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