Luca Martinazzi

Address

Department of Mathematics,
Rutgers University, NJ.
110 Frelinghuysen Road
Piscataway NJ 08854-8019
E.mail: martinazzi AT math.rutgers.edu


Teaching



Research


Fields of interest

  • Partial Differential Equations.
  • Geometric analysis.
  • Conformal geometry, Paneitz-GJMS operators, Q-curvature.
  • Calculus of variations.

Education

M.Sc. in Mathematics 05/2004 - Scuola Normale Superiore, Pisa
Title of the thesis: The non-parametric Plateau problem in arbitrary codimension.
Advisor: Prof. Mariano Giaquinta

Ph.D. in Mathematics 03/2009 - ETH Zurich
Title of the thesis: Concentration-compactness phenomena in conformal geometry
Advisor: Prof. Michael Struwe

CV


Publications and preprints

1. An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs
with M. Giaquinta. Edizioni della Normale, Pisa (2005). Buy

2. Classification of solutions to the higher order Liouville's equation on R^{2m}
Math. Z. 263 (2009), 307-329. Download, Journal

3. Conformal metrics on R^{2m} with constant Q-curvature
Rend. Lincei. Mat Appl. 19 (2008), 279-292. Download, Journal

4. Concentration-compactness phenomena in the higher order Liouville's equation
J. Funct. Anal. 256 (2009), 3743-3771. Download, Journal

5. A threshold phenomenon for embeddings of H^m_0 into Orlicz spaces
Calc. Var. Partial Differential Equations. 36 (2009), 493-506. Download, Journal

6. Concentration-compactness phenomena in conformal geometry
Ph.D. Thesis, March 2009. Download, DOI

7. Asymptotics and quantization for a mean-field equation of higher order
with M. Petrache. Comm. Partial Differential equations 35 (2010), 1-22. Download, Journal

8. Quantization for an elliptic equation of order 2m with critical exponential non-linearity
with M. Struwe. Math. Z. 270 (2012), 453-487. Download, Journal

9. Existence of solutions to a higher dimensional mean-field equation on manifolds
with M. Petrache. Manuscripta Math. 133 (2010), 115-130. Download, Journal

10. Quantization for the prescribed Q-curvature equation on open domains
Commun. Contemp. Math. 13 (2011), 533-551. Download, Journal

11. Gamma-convergence of nonlocal perimeter functionals
with L. Ambrosio and G. De Philippis. Manuscripta Math. 134 (2011), 377-403. Download, Journal

12. A note on quasilinear parabolic equations on manifolds
with C. Mantegazza. Preprint (2010). To appear in Ann. Scuola Norm. Sup. Pisa. Download

13. A note on n-axially symmetric harmonic maps from B^3 into S^2 minimizing the relaxed energy
Journal Funct. Analysis 261 (2011), 3099–3117. Download, Journal

14. Conformal metrics on R^2m with constant Q-curvature and large volume.
Preprint (2012). Download

15. Critical points of the Moser-Trudinger functional on a disk
with A. Malchiodi. Preprint (2012). Download

(Last updated: March 5, 2012)