Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6417036 | Journal of Differential Equations | 2016 | 29 Pages |
Abstract
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 Lâ 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Christoph Scheven, Thomas Schmidt,