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Higher Sobolev regularity for the fractional $p-$Laplace equation in the superquadratic case by Brasco, Lorenzo; Lindgren, Erik is a scholarly article available to read on EtoBox.

What is Higher Sobolev regularity for the fractional $p-$Laplace equation in the superquadratic case about?

We prove that for $p\ge 2$ 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 $W^{1,p}_{loc}$ and their gradients are in a fractional Sobolev space as well. The relevant estimates are stable as the fractional order of differentiation $s$ reaches $1$.

Author

Brasco, Lorenzo; Lindgren, Erik

Published

2015

Language

EN