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Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4309-9242
2017 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 304, 300-354 p.Article in journal (Refereed) Published
Abstract [en]

We prove that for p≥2, solutions of equations modeled by the fractional p-Laplacian improve their regularity on the scale of fractional Sobolev spaces. Moreover, under certain precise conditions, they are in Wloc 1,p and their gradients are in a fractional Sobolev space as well. The relevant estimates are stable as the fractional order of differentiation s reaches 1. © 2016 Elsevier Inc.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 304, 300-354 p.
Keyword [en]
Besov regularity, Fractional p-Laplacian, Nonlocal elliptic equations
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-195119DOI: 10.1016/j.aim.2016.03.039ScopusID: 2-s2.0-84986900072OAI: oai:DiVA.org:kth-195119DiVA: diva2:1048300
Note

Correspondence Address: Brasco, L.; Dipartimento di Matematica e Informatica, Università degli Studi di Ferrara, Via Machiavelli 35, Italy; email: lorenzo.brasco@unife.it. QC 20161121

Available from: 2016-11-21 Created: 2016-11-02 Last updated: 2016-11-21Bibliographically approved

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