Submitted Paper
Inserted: 10 feb 2020
Last Updated: 17 may 2020
Year: 2020
Abstract:
For $q>2, \gamma > 1$, we prove that maximal regularity of $L^q$ type holds for periodic solutions to
$-\Delta u +
Du
^{\gamma} = f$ in $\mathbb{R}^d$, under the (sharp) assumption $q > d \frac{\gamma-1}\gamma$.
Keywords: maximal regularity, Kardar-Parisi-Zhang equation, Riccati equation, Bernstein method
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