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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870815300876&_mathId=si1.gif&_user=111111111&_pii=S0001870815300876&_rdoc=1&_issn=00018708&md5=db13eec0418e2cb4a9d55b6b22e6e465" title="Click to view the MathML source">p≥2class="mathContainer hidden">class="mathCode">$p\ge 2$, 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 class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0001870815300876&_mathId=si2.gif&_user=111111111&_pii=S0001870815300876&_rdoc=1&_issn=00018708&md5=b32ef8908dd805a0ed52c576ea85e5e4">class="imgLazyJSB inlineImage" height="21" width="37" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0001870815300876-si2.gif">class="mathContainer hidden">class="mathCode">$W_{\mathit{loc}}^{1,p}$ 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.