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

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• 作者：Lorenzo Brasco^a ; ^b ; ^{lorenzo.brasco@unife.it" class="auth_mail" title="E-mail the corresponding author} ; Erik Lindgren^c ; ^{eriklin@kth.se" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35B65 ; 35J70 ; 35R09
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：2 January 2017
• 年：2017
• 卷：304
• 期：Complete
• 页码：300-354
• 全文大小：706 K

文摘

We prove that for p≥2$p\ge 2$, 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 $W_{\mathit{loc}}^{1,p}$ 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.