Marius Mitrea has worked on a variety of problems at the confluence of harmonic analysis, partial differential equations, and mathematical physics. He has delivered numerous talks at professional events around the world, and has supervised seven Masters and ten Ph.D. students. He has co-authored over 150 articles along with seven research monographs, including two monographs with Birkh\"auser and Springer in 2013. Marius Mitrea is the recipient of the 2014 Gold Chalk Award. He has been invited to give mini-courses in Padova, Italy, 2010, Instituto de Matem\'aticas Unidad Cuernavaca, Mexico, 2003, Tokyo, Japan, 2007, and UAM/Instituto de Ciencias Matematicas, Spain, 2012. Some of his distinguished addresses include plenary talks at:
- University of Arkansas' Spring Lecture Series, in 1993, 1996, 2000;
- International Conference on Clifford Analysis, its Applications to Mathematical Physics and Related Topics, Beijing, China, 2000;
- The 4th Rivi\'ere-Fabes Symposium, University of Minnesota, 2001;
- Plenary AMS Address, Orlando, Florida, November 2002;
- The Fabes-Chiarenza Lectures, Siracusa, Italy, 2002;
- The Midwest PDE Seminar, Purdue University, 2005;
- The 7-th International Conference on Dirac Operators and Mathematical Physics, Toulouse, France, 2005;
- The 6th International Congress of Romanian Mathematicians, Bucharest, Romania, 2007;
- The Second Workshop of Harmonic Analysis and Partial Differential Equations, Merida, Yucatan, Mexico, 2008;
- The James Clerk Maxwell Center, University of Edinburgh, Scotland, 2008;
- MSRI, Berkeley, 2008;
- The 10th International Conference on Integral Methods in Science and Engineering, Santander, Spain, 2008;
- The AMSI-ANU Workshop on Spectral Theory and Harmonic Analysis, The Australian National University, Canberra, Australia, 2009
- 1994 Ph.D., University of South Carolina
The research interests of Marius Mitrea include: Partial Differential Equations, Harmonic and Fourier Analysis, Complex and Clifford Analysis, Higher Dimensional Spectral Theory, Semigroup Theory, Geometric Measure Theory, Functional Analysis.
S. Hofmann, D. Mitrea, and A.J. Morris, Lp-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets, Memoirs of the American Mathematical Society, Vol. 245, No. 1159, 2017. ISBN: 1470422603; 9781470422608.
D. Mitrea, I. Mitrea, M. Mitrea, and M. Taylor, The Hodge-Laplacian: Boundary Value Problems on Riemannian Manifolds, Studies in Mathematics, Vol. 64, De Gruyter, 2016 (528 pages). ISBN: 3110484382; 9783110484380.
R. Alvarado and M. Mitrea, Hardy Spaces on Ahlfors-Regular Quasi-Metric Spaces. A Sharp Theory, Volume 2142, Lecture Notes in Mathematics, Springer, 2015, viii+486 pages, ISBN: 978-3-319-18131-8; 978-3-319-18132-5.
I. Mitrea and M. Mitrea, Multi-Layer Potentials and Boundary Problems for Higher-Order Elliptic Systems in Lipschitz Domains, Lecture Notes in Mathematics, Vol. 2063, Springer, 2013, Springer New York, Heidelberg, Dordrecht, London, x+424 pages, ISBN: 978-3-642-32665-3
D. Mitrea, I. Mitrea, M. Mitrea, and S. Monniaux, Groupoid Metrization Theory with Applications to Analysis on Quasi-Metric Spaces and Functional Analysis, Birkh\"auser, 2013, Springer New York, Heidelberg, Dordrecht, London, xii+479 pages, ISBN: 978-0-8176-8396-2.
M. Mitrea and M. Wright, Boundary Value Problems for the Stokes System in Arbitrary Lipschitz Domains, vii+241 pages, Ast\'erisque, Societ\'e Math\'ematique de France, Vol. 344, 2012. ISBN: 978-2-85629-343-0.
F. Gesztesy, and M. Mitrea, A description of all self-adjoint extensions of the Laplacian and Krein-type resolvent formulas on non-smooth domains. J. Analyse Math., 113 (2011), 53-172.
S. Hofmann, M. Mitrea, and M. Taylor, Singular Integrals and Elliptic Boundary Problems on Regular Semmes-Kenig-Toro Domains, International Mathematics Research Notices, Oxford University Press, 2010 (14), 2567--2865.
M. Ashbaugh, F. Gesztesy, M. Mitrea, and G. Teschl, Spectral theory for perturbed Krein Laplacians in nonsmooth domains. Adv. Math., 223 (2010), 1372-1467.
D. Mitrea, M. Mitrea, and M. Taylor, Layer Potentials, the Hodge Laplacian and Global Boundary Problems in Non-Smooth Riemannian Manifolds, Memoirs of the American Mathematical Society, Volume 150, Number 713, 2001, Providence RI, vii+120 pages, ISBN: 0-8218-2659-X.
M. Mitrea, Clifford Wavelets, Singular Integrals, and Hardy Spaces, Springer-Verlag Lecture Notes in Mathematics, No. 1575, Berlin, Heidelberg, New York 1994, xii+116 pages, ISBN: 3-540-57884-6.