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

created by goffi on 10 Feb 2020
modified on 14 Feb 2020

[BibTeX]

Preprint

Inserted: 10 feb 2020
Last Updated: 14 feb 2020

Year: 2020

ArXiv: 2001.11970 PDF

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 $q > d \frac{\gamma-1}\gamma$.