Calculus of Variations and Geometric Measure Theory

M. Cirant - A. Goffi

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

created by goffi on 10 Feb 2020
modified on 16 Jul 2021


Published Paper

Inserted: 10 feb 2020
Last Updated: 16 jul 2021

Journal: Archive for Rational Mechanics and Analysis
Volume: 240
Pages: 1521-1534
Year: 2020
Doi: 10.1007/s00205-021-01641-8

ArXiv: 2001.11970 PDF


In this paper we prove a conjecture by P.-L. Lions on maximal regularity of $L^q$-type for periodic solutions to $-\Delta u +
^\gamma = f$ 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