Research

Research interests

Harmonic analysis, Partial differential equations, Several complex variables, Cauchy-Riemann geometry, Geometric analysis, Inverse problems, Numerical analysis.

Preprints

  1. Ly Kim Ha, Tran Vu Khanh, and Andrew Raich - L^p-Estimates for the di-bar-equation on a class of infinite type domains. (pdf)
  2. Tran Vu Khanh - Lower bounds on the Kobayashi metric near a point of infinite type. (pdf)
  3. Tran Vu Khanh - Local estimates and hypoellipticity of the Kohn-Laplacian on pseudoconvex CR manifolds of infinity type.
  4. Tran Vu Khanh - Global hypoellipticity of the Kohn-Laplacian on pseudoconvex CR manifolds. pdf
  5. Tran Vu Khanh - A general estimates for the di-bar-Neumann problem. (pdf)

Publications

  1. Precise subelliptic estimates for a class of special domains (with Giuseppe Zampieri), J. Anal. Math. (accepted) (pdf).
  2. Lower bound for the geometric type from a generalized estimate in the $\dib$-Neumann problem - a new approach by peak functions, Michigan Math. J. (accepted) pdf.
  3. Hypoellipticity of the $\bar\partial$-Neumann problem at exponentially degenerate points (with Luca Baracco and Giuseppe Zampieri), Asian J. Math. (accepted) pdf.
  4. Loss of derivatives in the infinite type (with Stefanno Pinton and Giuseppe Zampieri), Pure Appl. Math. Q. (accepted)(pdf)
  5. Regularity at the boundary and tangential regularity of solutions of the Cauchy-Riemann system (with Giuseppe Zampieri). Pacific J. Math. (accepted). (pdf)
  6. Supnorm and f-Holder estimates for di-bar on convex domains of general type in C^2, J. Math. Anal. Appl. 430 (2013) 522-531 (pdf)
  7. Compactness of the di-bar-Neumann operator on q-pseudoconvex domain (with Giuseppe Zampieri). Complex Var. Elliptic Equ. 57 (2012) 1325-1337. (pdf)
  8. Propagation of regularity for solutions of the Kohn-Laplacian in a flat point (with Luca Baracco and Giuseppe Zampieri). Adv. Math. 230 (2012) 1972-1978. (pdf)
  9. Necessary geometric and analytic conditions for general estimates in the di-bar-Neumann problem (with Giuseppe Zampieri). Invent. Math. 188 (2012), 729-750.(pdf)
  10. Compactness estimates for b on CR manifolds (with Stefanno Pinton and Giuseppe Zampieri). Proc. Amer. Math. Soc. 140 (2012), 3229-3236.(pdf)
  11. Loss of derivatives for systems of complex vector fields and sums of squares (with Stefanno Pinton and Giuseppe Zampieri). Proc. Amer. Math. Soc. 140 (2012), 519-530.(pdf)
  12. Estimates for regularity of the tangential di-bar system (with Giuseppe Zampieri). Math. Nachr. 284 (2011), 2212-2224.(pdf)
  13. Subellipticity of the di-bar-Neumann problem on a weakly Q-pseudoconvex/concave domain (with Giuseppe Zampieri). Adv. Math. 228 (2011), 1938-1965.(pdf)
  14. Regularity of the di-bar-Neumannn problem at infinity type (with Giuseppe Zampieri). J. Funct. Anal. 259 (2010), 2760-2775.(pdf)
  15. Uniform regularity in a wedge and regularity of traces of CR functions (with Luca Baracco and Stefanno Pinton). J. Geom. Anal. 20 (2010), 996-1007.(pdf)
  16. The di-bar-Neumann problem. Seminario Dottorato 2009-2010, (2010), 10-18.(pdf)
  17. A nonlinear 1-D case backward heat problem : Regularization and error (with Dang Duc Trong, Pham Hoang Quan and Nguyen Huy Tuan). Z. Anal. Anwendungen 26 (2007), 231-245. (pdf)