The limiting normal cone to pointwise defined sets in Lebesgue spaces
P Mehlitz, G Wachsmuth - Set-Valued and Variational Analysis, 2018 - Springer
We consider subsets of Lebesgue spaces which are defined by pointwise constraints. We
provide formulas for corresponding variational objects (tangent and normal cones). Our
main result shows that the limiting normal cone is always dense in the Clarke normal cone
and contains the convex hull of the pointwise limiting normal cone. A crucial assumption for
this result is that the underlying measure is non-atomic, and this is satisfied in many
important applications (Lebesgue measure on subsets of R d R^d or the surface measure on …
provide formulas for corresponding variational objects (tangent and normal cones). Our
main result shows that the limiting normal cone is always dense in the Clarke normal cone
and contains the convex hull of the pointwise limiting normal cone. A crucial assumption for
this result is that the underlying measure is non-atomic, and this is satisfied in many
important applications (Lebesgue measure on subsets of R d R^d or the surface measure on …