Irina Mitrea

Contact Information

Research Interests:	Harmonic Analysis, PDE's, Geometric Measure Theory, Complex Analysis, Validated Numerics
Mailing Address:	Department of Mathematics Temple University 1805 N. Broad Street Philadelphia, PA 19122, USA
Office Location:	1020 Wachman Hall
E-mail Address:	imitrea(at)temple(dot)edu
Phone Number:	(215) 204-6741
Fax Number:	(215) 204-6433

List of publications:

The BMO-Dirichlet problem for elliptic systems in the upper-half space and quantitative characterizations of VMO, with José María Martell, D. Mitrea, and M. Mitrea, to appear in Analysis & PDE

Radiation conditions and integral representations for Clifford algebra-valued null-solutions of the Helmholtz operator, with E. Marmolejo-Olea, D. Mitrea, and M. Mitrea, Journal of Mathematical Sciences Vol. 231, Issue 3 (2018), 367-–472.

Hardy spaces of Clifford algebra-valued monogenic functions in exterior domains and a higher dimensional version of Cauchy's vanishing theorem, with E. Marmolejo-Olea, D. Mitrea, and M. Mitrea, Complex Var. Elliptic Equ. 62 (2017), no. 9, 1374--1392.

Invertibility properties of Singular Integral Operators associated with the Lamé and Stokes systems on infinite sectors in two dimensions, with K.Ott and W.Tucker, Integral Equations and Operator Theory, 89, No. 2 (2017), 151--207.

On the Lp-Poisson Semigroup Associated with Elliptic Systems, with José María Martell, D. Mitrea, and M. Mitrea, Potential Analysis, Vol. 47, No. 4 (2017), 401--445.

On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators, with H. Awala and K. Ott, to appear in Applied and Numerical Harmonic Analysis, 2017 (30 pages).

The Hodge-Laplacian; Boundary-Value Problems on Riemannian Manifolds, with D. Mitrea, M. Mitrea, and M. Taylor, De Gruyter Studies in Mathematics, No. 64, 2016 (516 pages).

The Dirichlet problem for elliptic systems with data in Köthe function spaces, with José María Martell, D. Mitrea, and M. Mitrea, Revista Matemática Iberoamericana, 268 (2016), 913--970.

Cauchy integrals, Calderón projectors, and Toeplitz operators on uniformly rectifiable domains, with M. Mitrea and M. Taylor, Advances in Mathematics, 268 (2015), 666--757.

Extending Sobolev functions with partially vanishing traces from locally (ε,δ)-domains and applications to mixed boundary problems, with K. Brewster, D. Mitrea, and M. Mitrea, Journal of Functional Analysis, 266 (2014), no. 7, 4314--4421.

The higher order regularity Dirichlet problem for elliptic systems in the upper-half space, with José María Martell, D. Mitrea, and M. Mitrea, Contemporary Mathematics, 612 (2014), 123--141.

Boundary value problems and integral operators for the bi-Laplacian in non-smooth domains, with M. Mitrea, Rendiconti Lincei: Matematica e Applicazioni, 24 (2013), 329--383.

Jones' extension operator on Sobolev spaces with partially vanishing traces, with K. Brewster, D. Mitrea, and M. Mitrea, Proceedings of Symposia in Pure Mathematics, Vol. 87 (2013), 59--69.

Whitney-Type Extensions in Quasi-Metric Spaces, with R. Alvarado and M. Mitrea, Communications on Pure and Applied Analysis, Vol. 12 (2013), no.1, 59--88.

Triebel-Lizorkin Sequence Spaces are Genuine Mixed-Norm Spaces, with D. Brigham, D. Mitrea, and M. Mitrea, Mathematische Nachrichten, Vol. 286 (2013), no. 5-6, 503--517.

Groupoid Metrization Theory with Applications to Analysis on Quasi-Metric Spaces and Functional Analysis, with D. Mitrea, M. Mitrea, and S. Monniaux, Applied and Numerical Harmonic Analysis, Birkhäuser, 2012 (479 pages).

Spectral Properties of the Reflection Operator in Two Dimensions, with K. Ott and E. Stachura, Contemporary Mathematics, Vol. 581 (2012) 199--215.

Stein's Extension Operator on Weighted Sobolev Spaces on Lipschitz Domains and Applications to Interpolation, with K. Brewster and M.Mitrea, Contemporary Mathematics, Vol. 581 (2012), 13--38.

Abstract capacitary estimates and the completeness and separability of certain classes of non-locally convex topological vector spaces, with D. Mitrea, M. Mitrea, and E. Ziadé, Journal of Functional Analysis, 262 (2012) 4766-4830.

Transmission Boundary Problems for Dirac Operators on Lipschitz Domains and Applications to Maxwell's and Helmholtz's Equations, with E. Marmolejo-Olea , M. Mitrea, and Q. Shi, Transactions of the AMS, Vol. 364, No. 8 (2012), 4369--4424.

Multi-Layer Potentials and Boundary Problems for Higher-Order Elliptic Systems in Lipschitz Domains, with M. Mitrea, Lecture Notes in Mathematics, Vol 2063, Springer-Verlag, 2012 (424 pages).

A Quantitative Open Mapping Theorem for Quasi-Pseudonormed Groups, with M. Mitrea and E. Ziadé, Recent Advances in Harmonic Analysis and Applications, a volume in honor of K.I. Oskolkov, Springer Proceedings in Mathematics, Vol. 25 (2013) 259--286.

On the Nature of the Laplace-Beltrami Operator on Lipschitz Manifolds, with F. Gesztesy, D. Mitrea, and M. Mitrea, Journal of Mathematical Sciences, New York Springer, Vol. 172 (2011), no. 3, 279--346.

Hodge Decompositions with Mixed Boundary Conditions and Applications to Partial Differential Equations on Lipschitz Manifolds, with Vladimir Gol'dshtein and M. Mitrea, Journal of Mathematical Sciences, New York Springer, Vol. 172 (2011), no. 3, 347--400.

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

Optimal Estimates for the Inhomogeneous Problem for the bi-Laplacian in Three Dimensional Lipschitz Domains, with M. Mitrea, and M. Wright, Journal of Mathematical Sciences, New York Springer, Vol. 172 (2011), no. 1, 24--134.

Spectral Theory and Iterative Methods for the Maxwell System in Nonsmooth Domains, with K. Ott, Mathematische Nachrichten, 283 (2010), no. 6, 784--804, Editor's Choice.

Mixed Boundary Value Problems for the Stokes System, with R. Brown, M. Mitrea, and M. Wright, Transactions of the American Mathematical Society, 362 (2010), no. 3, 1211--1230.

Regularity of the Green potential for the Laplacian with Robin boundary condition, with D. Mitrea, Integral Methods in Science and Engineering, Vol. 1, 235--243, Birkhäuser Boston, Inc., Boston, MA, 2010.

On the Dirichlet and regularity problems for the bi-Laplacian in Lipschitz domains, with M. Mitrea, Integral Methods in Science and Engineering, Vol. 1, 245--254, Birkhäuser Boston, Inc., Boston, MA, 2010.

Coercive energy estimates for differential forms in semi-convex domains, with D. Mitrea, M. Mitrea, and L. Yan, Communications on Pure and Applied Analysis, 9 (2010), no. 4, 987--1010.

Mapping Properties of Layer Potentials associated with Higher Order Elliptic Operators in Lipschitz Domains, Operator Theory: Advances and Applications, Vol. 203 (2009), 363--407.

The mixed problem for the Lamé system in a class of Lipschitz domains, with R. Brown, Journal of Differential Equations, 246 (2009), 2577-2589.

On the interplay between several complex variables, geometric measure theory and harmonic analysis, with M. Mitrea and M-C. Shaw, Revue Roumaine de Mathematiques Pures et Appliquees, 54 (2009), no. 5-6, 525--539.

On the regularity of differential forms satisfying mixed boundary conditions in a class of Lipschitz domains, with T. Jakab and M. Mitrea, Indiana University Mathematics Journal, 58 (2009), no 5, 2043--2072.

A Remark on the Regularity of the Div-Curl System, with M. Mitrea, Proceedings of the American Mathematical Society, 137 (2009), no. 5, 1729--1733.

Sobolev Estimates for the Green Potential Associated with the Robin-Laplacian in Lipschitz Domains satisfying a Uniform Exterior Ball Condition, with T. Jakab and M. Mitrea, Sobolev Spaces in Mathematics II, International Mathematical Series, Vol. 9, Springer Verlag, (2008), 227-260.

Traces of functions in Hardy and Besov spaces on Lipschitz domains with applications to compensated compactness and the theory of Hardy and Bergman type spaces, with T. Jakab and M. Mitrea, Journal of Functional Analysis, 246 (2007), 50--112.

Electromagnetic scattering from perturbed surfaces, with K. Ott , Mathematical Methods in the Applied Sciences 30 (2007), 861-876.

Interval Analysis Techniques for Boundary Value Problems of Elasticity in Two Dimensions, with W. Tucker , Journal of Differential Equations, 233 (2007), 181--198.

Counterexamples to the well-posedness of Lp transmission boundary value problems for the Laplacian, with K. Ott , Proceedings of the American Mathematical Society, 135 (2007), 2037-2043.

Boundary Problems for Harmonic Functions and Norm Estimates for Inverses of Singular Integrals in Two Dimensions, Numerical Functional Analysis and Optimization, 26 (2005), no. 7-8, 851--878.

The Poisson Problem with Mixed Boundary Conditions in Sobolev and Besov Spaces in Non-Smooth Domains, with M. Mitrea , Transactions of the American Mathematical Society, 359 (2007), 4143--4182.

The Dirichlet problem for elliptic systems in multiconnected rough regions, with S. S. Kulkarni and S. Mukherjee, Applicable Analysis, 84 (2005), no. 10, 971--988.

A Weakly Singular Integral Formulation for Displacement Prescribed Problems of Two-dimensional Elasticity, with S. S. Kulkarni and S. Mukherjee, Acta Mechanica, Vol. 176 (2005), 27-44.

Some Counterexamples for the Spectral Radius Conjecture, with W. Tucker, Differential and Integral Equations 16 (2003), no. 12, 1409--1439.

On the traction problem for the Lamé system on curvilinear polygons, J. Integral Equations and Applications, 16 (2004), no. 2, 175--218.

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

On the spectra of elastostatic and hydrostatic layer potentials on curvilinear polygons, J. Fourier Anal. Appl., 8 (2002), no. 5, 443--487.

Spectral radius properties for layer potentials associated with the elastostatics and hydrostatics equations in nonsmooth domains, J. Fourier Anal. Appl., 5 (1999), no. 4, 385--408.

On the boundedness of singular integrals, with E. Fabes and M. Mitrea , Pacific Journal of Mathematics, 189 (1999), no. 1, 21--29.

Monogenic Hardy spaces on Lipschitz domains and compensated compactness , with M.Mitrea , Complex Variables Theory Appl., 35 (1998), no. 3, 225--282.

Ph. D. Students and Postdocs:

Elia Ziadé, postdoc, Fall 2012 - Spring 2014.

Hussein Awala, graduate student, Spring 2013 - Summer 2017.

Katharine Ott, graduate student, Spring 2005 - May 2008.

Tunde Jakab , postdoc, Fall 2006 - Summer 2009.

Service and Outreach:

F12: Organizer of the conference Perspectives in Harmonic Analysis, Geometric Measure Theory, and Partial Differential Equations, and their applications to Several Complex Variables, September 13-15, 2012.

S06-S12: Girls and Mathematics Summer Program; 2011 edition at the IMA; 2008 Brochure ; 2007 Brochure; NBC News Coverage ; 2006 Brochure

2011-2013: Organizer (together with Maria Lorenz) of the Temple University Mathematics Circle.

2010-2014: Member of the Executive Committee of the Association for Women in Mathematics.

Spring 2009: Organizer of the conference Recent Advances in Harmonic Analysis and Elliptic PDE , May 8th-10th, 2009

Summer 2009: Lecturer at the 2009 Program for Women and Mathematics, Institute for Advanced Study, Princeton, June 8-19, 2009

Spring 2008: Coordinator for the Mathematics and Science Day for the Young Women Leaders Program , January 26, 2008

F07-S08: Organizer of the 2008 University of Virginia Mathematical Contest in Modeling; 2007 Edition;

F07-S09: MathCounts Coach for the Sutherland Middle School Mathematics Teams; 2009 Regional Competition Performance; 2008 Regional Competition Performance

S08: MathCounts at UVa Summer Program; 2008 Brochure

S07-F09: Organizer of the Sonia Kovalevsky Days: UVA SK Day , April 4, 2009; UVA SK Day, April 12, 2008; UVA SK Day , April 14, 2007; WPI SK Day, November 21st, 2009.

Spring 2007: The Thomas Jefferson and Mathematics Seminar ; University of Virginia, Program Poster

F06 - present: Organizer of the Undergraduate Mathematics Lecture Series:
- The Mathematics of Card Shuffling, Ken Brown (Cornell University), 11/10/06, Poster
- Can Computers Compute?, Warwick Tucker (Uppsala University), 03/14/07, Poster
- Cellular Automata with an Application to Biology, Jane Hawkins (University of North Carolina, Chapel Hill), 03/19/07 Poster
- Mathematical Paterns in Nature, John Adam (Old Dominion University), 05/18/07, Poster
- Take a Walk on the Boardwalk, Steve Abbott (Middlebury College), 09/13/07, Poster
- Fun, Ingenious, and Unusual Math, Dorina Mitrea (University of Missouri, Columbia), 03/20/09, Poster
- The Netflix Prize: how mathematics can predict the movies you'll love, Katharine Ott (University of Kentucky), 09/23/09, Poster
- Ruler, Compass and Origami Constructions: Trisecting an Angle and Doubling a Cube, Mike Hill (UVa and Harvard University), 09/30/09, Poster
- Implicit Stereotypes Matter in Math and Sciences, Fred Smyth (University of Virginia), 12/09/09, Poster
- Screening of the Documentary "Top Secret Rosies: The Female Computers of WWII", Producer/Director LeAnn Erickson (Temple University), 02/24/11, Poster
- Submajorization and the Geometry of Unordered Collections, with Applications to Music and Welfare Economics, Rachel Hall (St. Joseph's University), 02/24/12, Poster
- How to Build Graphs by Flipping Coins, and other Probabilistic Methods, Rehana Patel (Wesleyan University), 04/13/12, Poster
- A Mathematician Reads the Newspaper, John Allen Paulos (Temple University), 09/21/12, Poster
- Thirteen Ways Math and Poetry Connect, JoAnne Growney, 11/09/12, Poster

Links:

Google Scholar

E-JOURNALS (Mathematics and Statistics)

American Mathematical Society.

MathSciNet .

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