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arXiv · 2011.12407

A Fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations

Tadele Mengesha·James M. Scott
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Abstract

In this paper we prove a fractional analogue of the classical Korn's first inequality. The inequality makes it possible to show the equivalence of a function space of vector field characterized by a Gagliardo-type seminorm with 'projected difference' with that of a corresponding fractional Sobolev space. As an application, we will use it to obtain a Caccioppoli-type inequality for a nonlinear system of nonlocal equations, which in turn is a key ingredient in applying known results to prove a higher fractional differentiability result for weak solutions of the nonlinear system of nonlocal equations. The regularity result we prove will demonstrate that a well-known self-improving property of scalar nonlocal equations will hold for strongly coupled systems of nonlocal equations as well.

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Tadele Mengesha, James M. Scott. 2020-11-24. A Fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations. https://arxiv.org/abs/2011.12407

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