Dorina Mitrea, Ph.D.

Education

Ph. D., University of Minnesota, July 1996

Biography

Dr. Mitrea joined the Mathematics Department at Baylor University in August of 2019. 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.

Research

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).

Selected Journal Publications

Multi-layer potentials for higher-order systems in rough domains, Gustavo Hoepfner, Paolo Liboni, Dorina Mitrea, Irina Mitrea, and Marius Mitrea, Analysis and PDE, Vol. 14 (2021), no. 4, 1233-1308.

A sharp divergence theorem with nontangential traces, Dorina Mitrea, Irina Mitrea, and Marius Mitrea, Notices of AMS, Vol. 67 (2020), no. 9, 1295-1305.

The BMO-Dirichlet problem for elliptic systems in the upper-half space and quantitative characterizations of VMO, Jose Maria Martell, Dorina Mitrea, Irina Mitrea, and Marius Mitrea, Analysis and PDE, 12 (2019), no. 3, 605-720.

Characterizing regularity of domains via the Riesz Transforms on their boundaries, Dorina Mitrea, Marius Mitrea, and Joan Verdera, Analysis and PDE, Vol. 9, (2016), 955--1018.

Extending Sobolev functions with partially vanishing traces from locally (Ɛ,δ)-domains and applications to mixed boundary problems, Kevin Brewster, Dorina Mitrea, Irina Mitrea, and Marius Mitrea, Journal of Functional Analysis, 266 (2014), 4314--4421.

Hardy spaces and regularity for the inhomogeneous Dirichlet and Neumann problems, Xuan Duong, Steve Hofmann, Dorina Mitrea, Marius Mitrea, and Lixin Yan, Revista Matematica Iberoamericana, 29 (2013), no. 1, 183--236.

On the Regularity of Green Functions in Lipschitz Domains, Dorina Mitrea and Irina Mitrea, Communications in Partial Differential Equations, 36 (2011), no. 2, 304--327.

Boundary value problems for the Laplacian in convex and semiconvex domains, Dorina Mitrea, Marius Mitrea, and Lixin Yan, Journal of Functional Analysis, 258 (2010), 2507--2585.

A generalization of Dahlberg's theorem concerning the regularity of harmonic Green potentials, Dorina Mitrea, Transactions of the American Mathematical Society, 360 (2008), no. 7, 3771--3793.

On the Besov regularity of conformal maps and layer potentials on nonsmooth domains, Dorina Mitrea and Irina Mitrea, Journal of Functional Analysis, 201 (2003), 380--429.

Layer Potentials and Hodge Decompositions in Two Dimensional Lipschitz Domains, Dorina Mitrea, Mathematische Annalen, 322 (2002), no. 1, 75--101.

Research Monographs

Geometric Harmonic Analysis, Vol I: A Sharp Divergence Theorem with Nontangential Pointwise Traces, Dorina Mitrea, Irina Mitrea, and Marius Mitrea, 945 pp., Developments in Mathematics, 72, Springer Nature, Switzerland, 2022; ISBN-13: 978-3031059490.

Geometric Harmonic Analysis, Vol II: Function Spaces Measuring Size and Smoothness on Rough Sets, Dorina Mitrea, Irina Mitrea, and Marius Mitrea, 930 pp., Developments in Mathematics, 73, Springer Nature, Switzerland, 2023, ISBN-13: 978-3031137174.

Geometric Harmonic Analysis, Vol III: Integral Representations, Calderón-Zygmund Theory, Fatou Theorems, and Applications to Scattering, Dorina Mitrea, Irina Mitrea, and Marius Mitrea, 900 pp., Developments in Mathematics, 74, Springer Nature, Switzerland, 2023, ISBN-13: 978-3031227349.

Singular Integral Operators, Quantitative Flatness, and Boundary Problems, Juan Jose Marin, Jose Maria Martell, Dorina Mitrea, Irina Mitrea, and Marius Mitrea,
Progress in Mathematics Vol. 344, Birkhäuser/Springer Nature, Switzerland, 2022. viii+601 pp. ISBN-13: 978-3031082337.

Distributions, Partial Differential Equations, and Harmonic Analysis, 2nd edition, Dorina Mitrea, Universitext, Springer, 2019, 615 pp., ISBN-10: 3030032957, ISBN-13: 9783030032951.

Lp-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets, Steve Hofmann, Dorina Mitrea, Marius Mitrea, and Andrew Morris, Memoirs of AMS, Vol. 245, No. 1159, 2017.

The Hodge Laplacian: Boundary Value Problems on Riemannian Manifolds, Dorina Mitrea, Irina Mitrea, Marius Mitrea, and Michael Taylor, De Gruyter Studies in Mathematics, Vol. 64, 2016, 516 pp., ISBN: 978-3-11-048266-9.

Distributions, Partial Differential Equations, and Harmonic Analysis, Dorina Mitrea, Universitext, Springer, 2013, 482 pp., ISBN-13: 978-1461482079.

Groupoid Metrization Theory With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis, Dorina Mitrea, Irina Mitrea, Marius Mitrea, and Sylvie Monniaux, Birkhäuser, 2013, Springer New York, Heidelberg, Dordrecht, London (xii+479 pages, ISBN: 978-0-8176-8396-2, DOI: 10.1007/978-0-8176-8397-9).

Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates, Steve Hofmann, Guozhen Lu, Dorina Mitrea, Marius Mitrea, and Lixin Yan, Memoirs of the American Mathematical Society, 214, No. 1007, 2011.

Calculus Connections, Dorina Mitrea and Asma Harcharras, 308 pp. Prentice Hall, 2006.

Layer potentials, the Hodge Laplacian and global boundary problems in nonsmooth Riemannian manifolds, Dorina Mitrea, Marius Mitrea, and Michael Taylor, Memoirs of American Mathematical Society, Vol. 150, No. 713, 2001.