Georgia Institute of Technology College of Sciences

The Integration by Parts Formula, which is equivalent withthe DivergenceTheorem, is one of the most basic tools in Analysis. Originating in theworks of Gauss, Ostrogradsky, and Stokes, the search for an optimalversion of this fundamental result continues through this day and theseefforts have been the driving force in shaping up entiresubbranches of mathematics, like Geometric Measure Theory.In this talk I will review some of these developments (starting from elementaryconsiderations to more sophisticated versions) and I will discuss recentsresult regarding a sharp divergence theorem with non-tangential traces.This is joint work withDorina Mitrea and Marius Mitrea from University of Missouri, Columbia.