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

Nikolaos Roidos; Yuanzhen Shao

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

Analysis of PDEs 2024-03-22 v2

Authors: Nikolaos Roidos , Yuanzhen Shao

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.

Keywords

maximal lq-regularity nonlocal parabolic equations bessel potential spaces fractional porous medium equation kirchhoff equation variable coefficients

Cite

@article{arxiv.2103.16361,
  title  = {Maximal $L_q$-regularity of nonlocal parabolic equations in higher order Bessel potential spaces},
  author = {Nikolaos Roidos and Yuanzhen Shao},
  journal= {arXiv preprint arXiv:2103.16361},
  year   = {2024}
}

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29 pages

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