M. Cirant - A. Goffi

On the problem of maximal $L^q$-regularity for viscous Hamilton-Jacobi equations

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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