Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case

Lorenzo Brasco,Erik Lindgren

doi:10.1016/j.aim.2016.03.039

Higher Sobolev regularity for the fractional p-Laplace equation in the superquadratic case

Lorenzo Brasco, Erik Lindgren

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https://doi.org/10.1016/j.aim.2016.03.039

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Journal: Advances in Mathematics	Publication Date: Sep 10, 2016
Citations: 100	License type: publisher-specific-oa

Affiliation: Centrale Marseille, Aix-Marseille University, Institut Polytechnique de Bordeaux, French National Centre for Scientific Research, University of Ferrara, KTH Royal Institute of Technology

#Fractional Sobolev Space #Superquadratic Case + Show 8 more

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Abstract

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 Wloc1,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.

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