The dimension of semialgebraic subdifferential graphs
arXiv:1102.4050 · doi:10.1016/j.na.2011.07.040.
Abstract
Examples exist of extended-real-valued closed functions on whose subdifferentials (in the standard, limiting sense) have large graphs. By contrast, if such a function is semi-algebraic, then its subdifferential graph must have everywhere constant local dimension . This result is related to a celebrated theorem of Minty, and surprisingly may fail for the Clarke subdifferential.
30 pages