Higher differentiability in the context of Besov spaces for a class of nonlocal functionals

Mikil Foss; Joe Geisbauer

doi:10.3934/eect.2013.2.301

Article Contents

2013, Volume 2, Issue 2: 301-318. Doi: 10.3934/eect.2013.2.301

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Higher differentiability in the context of Besov spaces for a class of nonlocal functionals

Mikil Foss^1, and
Joe Geisbauer^1,

1.
University of Nebraskat-Lincoln, Department of Mathematics, 203 Avery Hall, PO BOX 880130, Lincoln NE 68588-0130

Received: October 31, 2012

Revised: December 31, 2012

Published: May 2013

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Abstract

The aim of this paper is to contribute to the nonlocal theory within the calculus of variations by studying two classes of nonlocal functionals. Since the nonlocal theory is not quite as developed as the local theory, a proof for the existence and uniqueness of minimizers is provided. However, the main result within the paper establishes the higher differentiability, in the context of Besov spaces, for minimizers of nonlocal functionals. This result is obtained under quadratic growth assumptions via the difference quotient method.

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Mathematics Subject Classification: Primary: 49N60, 49J99; Secondary: 45G15.

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References

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