Analysis Seminar on "A Sharp Divergence Theorem" by Dorina Mitrea (Baylor University, TX)
Title: A Sharp Divergence Theorem
Abstract: In this talk I will discuss a version of the Divergence Theorem for vector fields which may lack any type of continuity and for which the boundary trace is taken in a strong, nontangential pointwise sense. These features of our brand of Divergence Theorem make it an effective tool in dealing with problems arising in various areas of mathematics, including Harmonic Analysis, Complex Analysis, Potential Analysis, and Partial Differential Equations. A few such applications will be presented.
About the Speaker: Dorina Mitrea received her PhD in Mathematics from the University of Minnesota in 1996 under the direction of Eugene Fabes. She joined the Mathematics Department at Baylor University in August of 2019 as a Professor and Chair. Prior to Baylor she has been a faculty at the University of Missouri in Columbia for 23 years, where she held the Houchins Distinguished Professorship during September 2016 - July 2019. Teaching awards received include a University of Missouri Provost's Outstanding Junior Faculty Award and a University of Missouri Kemper Fellowship for Teaching Excellence Award. She has also been involved in outreach activities, including work with mathematics teachers, hosting math competitions for students, as well as training middle school and high school students for various math competitions. For her work with middle school students Professor Mitrea was recognized by the 43rd President of the United States, George W. Bush, in the Oval Office at the White House, on December 12, 2003. To date, Dr. Mitrea has advised nine Masters and Ph. D. students. Currently, she is an editor for Complex Variables and Elliptic Equations.
Professor Mitrea’s research is at the interface between Harmonic Analysis, Partial Differential Equations, Differential Geometry, and Geometric Measure Theory. Topics of focus in her research include: singular integral operators of Calderon-Zygmund type and their use as tools in the treatment of boundary value problems, the interplay between analysis and geometry, both in the Euclidean ambient, as well as in the setting of Riemannian manifolds, acoustic and electromagnetic scattering, functional analysis in nonlocally convex spaces, metrization theorems in topology, and algebraic structures in analysis (groupoids, Clifford algebras). She has authored or co-authored eight research monographs and books in mathematics and has written more than 60 research articles in mathematics.
Regarding today's talk, the recent publication would be an excellent reference A sharp divergence theorem with nontangential traces, Dorina Mitrea, Irina Mitrea, and Marius Mitrea, Notices of AMS, Vol. 67 (2020), no. 9, 1295-1305 which can be found online at https://www.ams.org/journals/notices/202009/rnoti-p1295.pdf
Contact Name: María Cristina Pereyra
Contact Email: firstname.lastname@example.org