Maximal $L_q$-regularity of nonlocal parabolic equations in higher order Bessel potential spaces

TL;DR

This paper proves maximal regularity results for fractional parabolic equations with variable coefficients in Bessel potential spaces, leading to higher order regularity and smoothing effects for specific nonlocal equations.

Contribution

It establishes maximal $L_q$-regularity in Bessel potential spaces for fractional parabolic equations with variable coefficients, a novel extension in this context.

Findings

Higher order regularity for fractional porous medium equations

Instantaneous smoothing effects for nonlocal Kirchhoff equations

Maximal $L_q$-regularity results in Bessel potential spaces

Abstract

We consider fractional parabolic equations with variable coefficients and establish maximal $L_{q}$-regularity in Bessel potential spaces of arbitrary nonnegative order. As an application, we show higher order regularity and instantaneous smoothing for the fractional porous medium equation and for a nonlocal Kirchhoff equation.