Nonlocal fractional elliptic and parabol{\i}c equat{\i}ons in Besov spaces and applications

TL;DR

This paper investigates the regularity and well-posedness of nonlocal fractional elliptic and parabolic equations within Besov spaces, demonstrating sectoriality, semigroup generation, and maximal regularity properties.

Contribution

It establishes sectoriality and analytic semigroup generation for nonlocal fractional operators in Besov spaces, advancing understanding of their regularity and well-posedness.

Findings

Operator is sectorial in Besov spaces

Generated operator forms an analytic semigroup

Proves well-posedness of nonlocal fractional parabolic equations

Abstract

The maximal B_{p,q}^{s}-regularity properties of a nonlocal fractional elliptic equation is studied. Particularly, it is proven that the operator generated by this nonlocal ell{\i}p{\i}t{\i}c equation in B_{p,q}^{s} is sectorial and also is a generator of an analytic semigroup. Moreover, well-posedeness of nonlocal fractional parabolic equation in Besov spaces are established.