Photo from wikipedia
In this paper we prove the rectifiability of and measure bounds on the singular set of the free boundary for minimizers of a functional first considered by Alt-Caffarelli. Our main… Click to show full abstract
In this paper we prove the rectifiability of and measure bounds on the singular set of the free boundary for minimizers of a functional first considered by Alt-Caffarelli. Our main tools are the Quantitative Stratification and Rectifiable-Reifenberg framework of Naber-Valtorta, which allow us to do a type of "effective dimension-reduction." The arguments are sufficiently robust that they apply to a broad class of related free boundary problems as well.
Keywords:
quantitative stratification;
stratification free;
boundary problems;
free boundary
Journal Title: Transactions of the American Mathematical Society
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!
Journal Title: Transactions of the American Mathematical Society
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!