An epiperimetric inequality approach to the regularity of the free boundary in the Signorini problem with variable coefficients

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• 作者：Nicola Garofalo^a ; ¹ ; ^{nicola.garofalo@unipd.it" class="auth_mail" title="E-mail the corresponding author} ; Arshak Petrosyan^b ; ² ; ^{arshak@math.purdue.edu" class="auth_mail" title="E-mail the corresponding author} ; Mariana Smit Vega Garcia^c ; ³ ; ⁴ ; ^{mariana.vega-smit@uni-due.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J35 ; 35J20 ; 35J65
• 刊名：Journal de mathematiques pures et appliquees
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：105
• 期：6
• 页码：745-787
• 全文大小：679 K

文摘

In this paper we establish the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021782415001634&_mathId=si1.gif&_user=111111111&_pii=S0021782415001634&_rdoc=1&_issn=00217824&md5=26152b201068f3022b1954d354354897" title="Click to view the MathML source">C^1,βclass="mathContainer hidden">class="mathCode">$C^{1,\beta }$ regularity of the regular part of the free boundary in the Signorini problem for elliptic operators with variable Lipschitz coefficients. This work is a continuation of the recent paper [12], where two of us established the interior optimal regularity of the solution. Two of the central results of the present work are a new monotonicity formula and a new epiperimetric inequality.