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arXiv · 1901.02507

Equivalence of viscosity and weak solutions for a $p$-parabolic equation

Jarkko Siltakoski
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Abstract

We study the relationship of viscosity and weak solutions to the equation \[ \smash{\partial_{t}u-\Delta_{p}u=f(Du)} \] where $p>1$ and $f\in C(\mathbb{R}^{N})$ satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when $p\geq2$.

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Jarkko Siltakoski. 2019-01-08. Equivalence of viscosity and weak solutions for a $p$-parabolic equation. https://arxiv.org/abs/1901.02507

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