Luca Martinazzi

Address

Department of Mathematics Guido Castelnuovo,
Università di Roma La Sapienza, Italy.
Piazzale Aldo Moro 5
I-00185, Roma
E.mail: luca.martinazzi AT uniroma1.it

CV

Fields of interest

  • Partial Differential Equations.
  • Geometric analysis.
  • Conformal geometry, Paneitz-GJMS operators, Q-curvature.
  • Nonlocal equations (fractional Laplacian, nonlocal minimal surfaces)
  • Harmonic maps
  • Moser-Trudinger inequality.
  • Calculus of variations, variational and topological methods.

Publications and preprints

Monographs

Il problema di Plateau non parametrico in codimensione arbitraria
Master Thesis, Pisa, May 2004. Italian, English, Università di Pisa.
Concentration-compactness phenomena in conformal geometry
Ph.D. Thesis, Zurich, March 2009. Download, ETH library
An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs, 2nd Edition
with M. Giaquinta. Edizioni della Normale, Pisa 2012 (1st edition, 2005). Preview.
Price: around 25EUR/30USD. Buy here

Papers


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

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

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

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

An application of Q-curvature to an embedding of critical type
Oberwolfach Reports 6 (2009), 1997-2000. Download, Journal

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

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

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

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

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

A note on quasilinear parabolic equations on manifolds
with C. Mantegazza. Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (5), Vol. XI (2012), 1-18. Download, Journal

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

Conformal metrics on R^2m with constant Q-curvature and large volume
Ann. Inst. Henri Poincaré (C) 30 (2013), 969-982. Download, Journal

Critical points of the Moser-Trudinger functional on a disk
with A. Malchiodi. J. Eur. Math. Soc. (JEMS) 16 (2014), 893-908. Download, Journal

Existence and asymptotics for solutions of a non-local Q-curvature equation in dimension three
with T. Jin, A. Maalaoui, J. Xiong. Calc. Var. Partial Differential Equations 52 (2015), 469-488. Download, Journal

Conformal metrics on R^2m with constant Q-curvature, prescribed volume and asymptotic behavior
with A. Hyder. Discr. Cont. Dynamical Systems - A 35 (2015), 283-299. Download, Journal

Blow-up analysis of a nonlocal Liouville-type equation
with F. Da Lio, T. Riviere. Analysis and PDE 8 (2015), 1757-1805. Download, Journal

Blow-up behaviour of a fractional Adams-Moser-Trudinger type inequality in odd dimension
with A. Maalaoui, A. Schikorra, Comm. Partial Differential Equations 41 (2016), 1593-1618. Download, Journal.

A fractional Moser-Trudinger type inequalitiy in one dimension and its critical points
with A. Maalaoui, S. Iula, Differential and Integral Equations 29 (2016), 455-492. Download, Journal

Fractional Adams-Moser-Trudinger inequalities
Nonlinear Analysis 127 (2015), 263-278. Download, Journal

The nonlocal Liouville-type equation in R and conformal immersions of the disk with boundary singularities
with F. Da Lio, Calc. Var. Partial Differential Equations (2017), 56:152. Download, Journal.

The Moser-Trudinger inequality and its extremals on a disk via energy estimates
with G. Mancini, Calc. Var. Partial Differential Equations (2017), 56:94. Download, Journal.

Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space
with A. Hyder, S. Iula, Commun. Contemp. Math. 20 (2018), 1750026 Download, Journal.

Gluing metrics with prescribed Q-curvature and different asymptotic behaviour in dimension 6
with A. Hyder, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. 22 (2021), 505-547, arXiv, Journal.

Concentration phenomena for the fractional Q-curvature equation in dimension 3 and fractional Poisson formulas
with A. DelaTorre, M. del Mar Gonzalez, A. Hyder, J. London Math. Soc. 104 (2021) arXiv, Journal.

The non-local mean-field equation on an interval
withA. de la Torre, A. Hyder, Y. Sire, Commun. Contemp. Math. 1950028 (2019) arXiv, Journal.

Local and nonlocal singular Liouville equations in Euclidean spaces
with A. Hyder, G. Mancini, Intern. Math. Res. Notices (2019) arXiv, Journal.

Extremals for fractional Moser-Trudinger inequalities in dimension 1 via harmonic extensions and commutator estimates
with G. Mancini, Adv. Nonlin. Studies 20 (2020), 599-632 arXiv, Journal.

Critical points of the Moser-Trudinger functional on closed surfaces
with F. De Marchis, A. Malchiodi, P-D. Thizy, preprint (2020) arXiv.

Normal conformal metrics on R4 with Q-curvature having power-like growth
with A. Hyder, J. Diff. Equ. 282 (2021) arXiv, Journal.

Sign-changing blow-up for the Moser-Trudinger equation in R2
with P.-D. Thizy and J. Vetois, J. Funct. Anal. 282 (2022), 109288 arXiv, Journal.

Critical points of the Moser-Trudinger functional on closed surfaces
with F. De Marchis, A. Malchiodi, P-D. Thizy, Invent. Math. 230 (2022), 1165-1248 arXiv, Journal.

Critical points of arbitrary energy for the Trudinger- Moser embedding in planar domains
with A. Malchiodi, P-D. Thizy, Adv. Math (to appear), preprint (2022), arXiv.


(Last updated: February 2024)