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- W4297772618 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." @default.
- W4297772618 created "2022-10-01" @default.
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- W4297772618 date "2020-11-24" @default.
- W4297772618 modified "2023-09-26" @default.
- W4297772618 title "A Fractional Korn-type inequality for smooth domains and a regularity estimate for nonlinear nonlocal systems of equations" @default.
- W4297772618 doi "https://doi.org/10.48550/arxiv.2011.12407" @default.
- W4297772618 hasPublicationYear "2020" @default.
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