[Plenary Lecture] Curl-measure Fields and The Stokes' Theorem for Weakly Differentiable Vector Fields

2nd OIST-Oxford-SLMath Summer Graduate School on Analysis and Partial Differential Equations

Time: June 26 (Fri) 1:00 pm - 2:00 pm

Speaker: Prof. Monica Torres (Purdue University)

Title: Curl-measure Fields and The Stokes' Theorem for Weakly Differentiable Vector Fields

Abstract: We introduce and analyze the class of curl-measure fields, consisting of p-integrable vector fields whose distributional curl is a vector-valued finite Radon measure. These spaces provide a unifying framework for the study of problems involving vorticity. We establish Stokes-type theorems for curl-measure fields by introducing Stokes functionals on good manifolds, characterized through the finitness of manifold-adapted maximal operators, and by applying new trace theorems for curl-measure fields.