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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang

IMPACT FACTOR 2017: 1.676

CiteScore 2017: 1.30

SCImago Journal Rank (SJR) 2017: 2.045
Source Normalized Impact per Paper (SNIP) 2017: 1.138

Mathematical Citation Quotient (MCQ) 2017: 1.15

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Volume 8, Issue 4


On a new class of fractional partial differential equations

Tien-Tsan Shieh / Daniel E. Spector
Published Online: 2014-05-29 | DOI: https://doi.org/10.1515/acv-2014-0009


In this paper, we study a new class of fractional partial differential equations which are obtained by minimizing variational problems in fractional Sobolev spaces. We introduce a notion of fractional gradient which has the potential to extend many classical results in the Sobolev spaces to the nonlocal and fractional setting in a natural way.

Keywords: Fractional gradient; fractional Sobolev inequalities; fractional partial differential equations; Bessel potential spaces

MSC: 26A33; 35R11; 49J45; 35JXX

About the article

Received: 2013-11-23

Revised: 2014-04-11

Accepted: 2014-04-11

Published Online: 2014-05-29

Published in Print: 2015-10-01

Funding Source: National Science Council of Taiwan

Award identifier / Grant number: NSC-101-2115-M-009-014-MY3

Funding Source: Technion

Award identifier / Grant number: Fellowship

Citation Information: Advances in Calculus of Variations, Volume 8, Issue 4, Pages 321–336, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2014-0009.

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