Maximal $L_q$-regularity of nonlocal parabolic equations in higher order 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.

29 pages

References in corpus (2)

• Singular parabolic equations of second order on manifolds with singularities
• Wellposedness of a nonlocal nonlinear diffusion equation of image processing