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

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

11 pages