Recent Papers (2000-2003)

• Sharp Hodge Decompositions, Maxwell's Equations, and Vector Poisson Problems on Non-Smooth, Three-Dimensional Riemannian Manifolds Duke Mathematical Journal to appear, (2004) [psfile] [pdffile]
   
• Layer Potentials and Boundary Value Problems for Laplacian in Lipschitz Domains with Data in Quasi-Banach Besov Spaces (with S. Mayboroda) Annali Di Matematica Pura Ed Applicata to appear, (2004) [psfile] [pdffile]
   
• Sobolev and Besov space estimates for solutions to second order PDE on Lipschitz domains in manifolds with Dini or Hölder continuous metric tensors (with M. Taylor) Communications in PDE to appear, (2004) [psfile] [pdffile]
   
• Transmission problems and spectral theory for singular integral operators on Lipschitz domains (with L. Escauriaza) Journal of Functional Analysis to appear, (2004) [psfile] [pdffile]
   
• Square Function Estimates for Singular Integrals and Applications to Partial Differential Equations (with S. Mayboroda) Differential and Integral Equations to appear, (2004) [psfile] [pdffile]
   
• Spectral properties of parabolic layer potentials and transmission boundary problems in nonsmooth domains (with S. Hofmann and J. Lewis) Illinois Journal of Mathematics to appear, (2003) [psfile] [pdffile]
   
• The stationary Navier-Stokes system in nonsmooth manifolds: the Poisson problem in Lipschitz and C1 domains (with M. Dindos) Archive for Rational Mechanics and Analysis to appear, (2003) [psfile] [pdffile]
   
• Sharp Hodge decompositions in two and three dimensional Lipschitz domains (with D. Mitrea) Comptes Rendus de l'Academie des Sciences, Paris, Ser. I, Math., Vol. 334 (2002), 109--112 [psfile] [pdffile]
   
• Boundary-value problems for Dirac Operators and Maxwell's equations in  nonsmooth domains Math. Methods Appl. Sci. Vol.25 (2002), no. 16-18, 1355--1369. [ psfile] [ pdffile]
   
• Poisson problems with half-Dirichlet boundary conditions for Dirac operators on nonsmooth manifolds (with D. Mitrea) Memoirs on Differential Equations and Mathematical Physics, Vol.30 (2003), 9--49. [ psfile] [ pdffile]
   
• Potential theory on Lipschitz domains in Riemannian manifolds: the case of Dini metric tensors (with M. Taylor) Trans. Amer. Math. Soc., Vol.355 (2003), no. 5, 1961--1985 [ psfile] [ pdffile]
   
• Harmonic analysis for general first order differential operators in Lipschitz domains (with E. Marmolejo-Olea) Clifford Algebras: Application to Mathematics, Physics, and Engineering Birkhauser Progress in Mathematical Physics Series, 2003, pages 91--114. [ psfile] [ pdffile]
   
• Navier-Stokes Equations on Lipschitz Domains in Riemannian Manifolds (with M. Taylor) Math. Annalen Vol. 321 (2001), no. 4,  955-987 [ psfile] [ pdffile]
   
• A note on Besov regularity of layer potentials and solutions of elliptic PDE's Proc. Amer. Math. Soc., Vol. 130 (2002), 2599-2607 [psfile]  [pdffile]
   
• The Initial Dirichlet Boundary Value Problem for General  Second Order Parabolic Systems in Nonsmooth Manifolds Communications in PDE , Vol. 26 (2001), no. 11-12, 1975--2036 [ psfile]  [pdffile]
   
• General Second Order, Strongly Elliptic Systems in Low Dimensional Nonsmooth Manifolds (with D. Mitrea) Contemporary Math., Vol.277 (2001), 61-86 [ psfile]  [pdffile]
   
•  Potential theory on Lipschitz domains in Riemannian manifolds:  Holder continuous metric tensors (with M. Taylor) Communications in PDE , Vol.25 (2000), 1487-1536 [ psfile]  [pdffile]
   
• Dirichlet integrals and Gaffney-Friedrichs inequalities in convex domain Forum Math., Vol.13 (2001), 531-567 [ psfile]  [pdffile]
   
• Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem (with M. Taylor) J. Funct. Anal., Vol.176 (2000), 1-79   [psfile]  [pdffile]
   
• The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations (with O. Mendez) Journal of Fourier Analysis and Applications, Vol.6 (2000), 503-531 [ psfile]  [pdffile]
   
• The method of layer potentials for electromagnetic waves in chiral media Forum Math., Vol.13 (2001), 423-446 [ psfile]  [pdffile]
   
• Complex powers of the Neumann Laplacian in Lipschitz domains (with O. Mendez) Mathematische Nachrichten, Vol.223 (2001), 77-88  [ psfile]  [pdffile]
   
• Extension and representation of divergence free vector fields on bounded domains  (with T. Kato, G. Ponce and M. Taylor) Math. Research Letters, Vol.7 (2000), 643-650  [psfile]  [pdffile]
   
• Generalized Dirac operators  on nonsmooth manifolds and Maxwell's equations Journal of Fourier Analysis and Applications, Vol.7 (2001), 207-556 [psfile]  [pdffile]
   
• Potential theory on Lipschitz domains in Riemannian manifolds: Lp, Hardy and Holder type results  (with M. Taylor) Communications in Analysis and Geometry, Vol.9 (2001), 369-421 [psfile]  [pdffile]
   
• Semilinear  Poisson problems on Sobolev-Besov spaces on Lipschitz domains (with M. Dindos) Publ. Mat. Vol.46 (2002), no. 2, 353--403 [psfile]  [pdffile]
   
• The oblique derivative problem for general elliptic systems in Lipschitz domains Integral Methods in Science and Engineering, CRC 2001, Vol.418,  pp.240-245  [psfile]  [pdffile]
   
• Finite energy solutions of Maxwell's equations and constructive Hodge decompositions on nonsmooth Riemannian manifolds (with D. Mitrea) J. Funct. Anal. Vol.190 (2002), no. 2, 339--417 [ psfile] [pdffile]
   
• Higher degree layer potential operators in Lipschitz  domains (with D. Mitrea) Integral Equations and Operator Theory, Vol.37, No.4 (2000), 457-486 [psfile] [pdffile]
   
• Layer potentials, the Hodge Laplacian and global  boundary problems in non-smooth Riemannian manifolds (with D. Mitrea and M. Taylor) Memoirs of the American Mathematical Society, ISSN: 0065-9266, Volume 150, Number 713 (4th of 5 numbers), 2001, Providence RI, vii+120 pages, ISBN: 0-8218-2659-X

Other Selected Publications

• Clifford Wavelets, Singular Integrals, and Hardy Spaces Lecture Notes in Mathematics No.1575,  Springer-Verlag, Berlin/ Heidelberg/ New York 1994 xii+116 pages, ISBN: 3-540-57884-6
   
• Electromagnetic scattering on nonsmooth domains Mathematical Research Letters, Vol.1, No.6 (1994),  639-646
   
•  On Dahlberg's Lusin area integral theorem Proceedings of the American Mathematical Society, Vol.123, No.5 (1995), 1449-1455
   
• The method of layer potentials in electro-magnetic  scattering theory on non-smooth domains Duke Mathematical  Journal, Vol.77, No.1 (1995), 111-133
   
•  Boundary estimates for harmonic forms(with T. Iwaniec and C. Scott) Proc. of Amer. Math. Soc., Vol.124, No.5, (1996), 1467-1471
   
• Higher dimensional scattering theory on C1 and Lipschitz domains (with B. Jawerth) American Journal of  Mathematics, Vol.117, No.4 (1995), 929-963
   
• Pluridimensional absolute continuity for differential forms and the Stokes formula (with M. Jurchescu) L'Enseignement Mathematique, Vol.41, No.3-4 (1995),  217-255.
   
• Initial boundary value problems for the parabolic  Maxwell system in Lipschitz cylinders Indiana University  Mathematics Journal, Vol.44, No.3 (1995), 797-813
   
• Vector potential theory on Lipschitz domains in R3 and applications to electromagnetic scattering (with D. Mitrea and J. Pipher) The Journal of Fourier Analysis  and Applications, Vol.3, No.2, (1997), 131-192
   
•  Boundary integral methods for harmonic differential  forms in Lipschitz domains, (with D. Mitrea) Electronic Research Announcements of the Amer. Math. Soc., Vol.2, No.2 (1996),  92-97
   
• Stability of Fredholm properties on interpolation scales of quasi-Banach spaces and applications (with N. Kalton) Transactions of the Amer. Math. Soc., Vol.350, No.10 (1998), 3903-3922
   
• Pompeiu's integral representation formula. History and Mathematics (with F. Sabac) Revue Roumaine de  Mathematiques Pures et Appliquees, Vol.43 No.1-2 (1998),  211-226
   
•  Boundary layer methods for Lipschitz domains in Riemannian  manifolds (with M. E. Taylor) Journal of Functional Analysis, Vol.163 (1999),  181-251
   
• Uniqueness for inverse conductivity and transmission problems in the class of Lipschitz domain (with D. Mitrea) Communications in Partial Differential Equations, Vol.23 No.7-8, (1998), 1419-1448
   
•  Potential operators on Besov spaces and the Poisson  equation with Dirichlet and Neumann boundary conditions on Lipschitz domains (with E. Fabes and O. Mendez)  Journal of Functional Analysis, Vol.159, No.2 (1998), 323-368
   
•  On the boundedness of singular integrals (with E. Fabes and I. Mitrea) Pacific Journal of Mathematics, Vol.189,  No.1 (1998),  21-29
   
•  On Bojarski's index formula for nonsmooth interfaces Electronic Research Announcements of the Amer. Math. Soc., Vol.5, No.1 (1999),  40-46
   
•  Clifford algebras and Maxwell's equations in Lipschitz  domains (with A. McIntosh) Mathematical Methods in the Applied  Sciences, Vol.22, No.18 (1999), 1599-1620
   
• The Cauchy singular integral operator and Clifford wavelets (with L. Andersson and B. Jawerth) Wavelets: Mathematics and Applications, pp.525-546, Stud. Adv. Math., CRC,  1994