Irina Mitrea               

Contact Information

List of publications:

• On the Nature of the Laplace-Beltrami Operator on Lipschitz Manifolds, with Fritz 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:

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