BV supersolutions to equations of 1-Laplace and minimal surface type

详细信息    查看全文

• 作者：Christoph Scheven^a ; ^{christoph.scheven@uni-due.de" class="auth_mail" title="E-mail the corresponding author} ; ; Thomas Schmidt^b ; ^c ; ^{thomas.schmidt@math.uni-hamburg.de" class="auth_mail" title="E-mail the corresponding author} ;
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 August 2016
• 年：2016
• 卷：261
• 期：3
• 页码：1904-1932
• 全文大小：465 K

文摘

We propose notions of BV supersolutions to (the Dirichlet problem for) the 1-Laplace equation, the minimal surface equation, and equations of similar type. We then establish some related compactness and consistency results.

Our main technical tool is a generalized product of cdca22d1aea68ed4" title="Click to view the MathML source">L^∞${\mathrm{L}}^{\infty }$ divergence-measure fields and gradient measures of BV functions. This product crucially depends on the choice of a representative of the BV function, and the proofs of its basic properties involve results on one-sided approximation and fine (semi)continuity in the BV context.