Publications:
- M. González. Singular sets of a class of locally conformally
flat manifolds. Duke Mathematical Journal, 129, no. 3
(2005), 551–572 .pdf
- M. González. Removability of singularities for a class of
fully non-linear elliptic equations. Calc.Var. and PDE, 27
(2006), no. 4, 439–466 .pdf
- M. González. Classification of singularities for a subcritical
fully non-linear problem. Pacific J. Math. 226 (2006), no. 1,
83–102 .pdf
- M. González, M. Gualdani. Asymptotics for a symmetric equation
in price formation. App. Math. Optim. 59 (2009), 233–246
.pdf
- M. González. Gamma convergence of an energy functional related
to the fractional Laplacian. Calc.Var. and PDE, 36 (2009), no.
2, 173-210
.pdf
- L. Chayes, M. Gualdani, I. Kim. Global existence and
uniqueness of solutions to a model of price formation. SIAM J.
Math. Anal. Volume 41, Issue 5, pp. 2107-2135 (2009)
.pdf
- S.-Y. A. Chang, M. González. Fractional Laplacian in conformal
geometry. Advances in Mathematics,Volume 226, Issue 2, pages
1410-1432, (2011) .pdf
- M. González, M. Gualdani. Asymptotics for a free-boundary
model in price formation. Nonlinear Analysis: Theory, Methods
& Applications, 74 (2011), 3269–3294 .pdf
- M. González. R. Monneau. Slow motion of particle systems as a
limit of a reaction-diffusion equation with fractional
Laplacian. Discrete and Continuous Dynamical Systems - A, Vol.
32, no. 4 (2012), 1255-1286.
.pdf
- M. González, R. Mazzeo, Y. Sire. Singular solutions of
fractional order conformal Laplacians. Journal of Geometric
Analysis 22 (2012), no. 3, 845-863 .pdf
- M. González, M. Gualdani. Some non-standard Sobolev spaces:
interpolation and its application to PDE. Acta Applicanda
Mathematicae 121, no. 1 (2012), 57-67 .pdf
- M. González. A weighted notion of renormalized volume related
to the fractional Laplacian. Pacific J. Math. Vol. 257, no. 2
(2012), 379-394 .pdf
- J. Carrillo, M. González, M. Gualdani, M. Schonbek. Classical
solutions for a nonlinear Fokker-Planck equation arising in
Computational Neuroscience. Comm. in PDE 38, 385–409
(2013) .pdf
- M. González, J. Qing. Fractional conformal Laplacians and
fractional Yamabe problems. Analysis & PDE 6 (2013), no. 7,
1535-1576 .pdf
- L. Caffarelli, M. González, T. Nguyen. A perturbation argument
for a Monge-Ampere type equation arising in optimal
transportation. Arch. Rat. Mech. Anal. 212, no. 2 (2014)
359–414 .pdf
- M. González, M. Gualdani, H. Shahgholian. A discrete Bernoulli
free boundary problem. Proceedings of the St. Petersburg
Mathematical Society. Vol XV. Advances in mathematical analysis
of partial differential equations, 119–140, Amer. Math.
Soc.Transl. ser. 2, 232, Amer. Math Soc., Providence, RI,
2014.
.pdf
- M. González, L. Mazzieri. Singularities for a fully non-linear
elliptic equation in conformal geometry. Bull. Inst. Math.
Academia Sinica (New Series), Vol. 9 (2014), No. 2, pp. 223-244
.pdf
- M. González, M. Sáez, Y. Sire. Layer solutions for the
fractional Laplacian on hyperbolic space. Annali di Matematica
Pura ed Applicata, Vol 193, no.6 (2014), 1823-1850.
.pdf
- V. Banica, M. González, M. Sáez. Some constructions for the
fractional Laplacian on noncompact manifolds. Rev. Mat. Iberoam.
31 (2015), no. 2, 681–712 .pdf
- R. Frank, M. González, D. Monticelli, J. Tan. An extension
problem for the CR fractional Laplacian. Advances in
Mathematics, 270 (2015) 97–137 .pdf
- Y. Fang, M. González. Asymptotic behavior of Palais-Smale
sequences associated with fractional Yamabe type
equations. Pacific J. Math, 278, No. 2 (2015) 369-405
.pdf
- M. González. M. Gualdani, J. Solŕ-Morales. Instability and
bifurcation in a trend depending price formation model. Acta
Applicanda Mathematicae 144, n. 1 (2016), 121-136
.pdf
- A. DelaTorre, M. del Pino, M. González, J. Wei. Delaunay-type
singular solutions for the fractional Yamabe problem.
Mathematische Annalen 369 (2017) no. 1-2,
597–626 .pdf
- A. Enciso, M. González, B. Vergara. Fractional powers of the
wave operator via Dirichlet-to-Neumann maps in anti-de Sitter
spaces. Journal of Functional Analysis 273 (2017), no. 6,
2144–2166 .pdf
- E. Cinti, B. Franchi, M. González. Gamma-convergence of
variational functionals with boundary terms in Stein manifolds.
Calc. Var. and PDE 56 (2017), no. 6, Art. 155, 52 pp.
.pdf
- M. González, M. Wang. Further results on the fractional
Yamabe problem: the umbilic case. Journal of Geometric Analysis
28 (2018), 22–60 .pdf
- M. González, M. Sáez. Fractional Laplacians and extension
problems: the higher rank case. Trans. Amer. Math. Soc.
370 (2018), no. 11, 8171–8213 .pdf
- M. González. Recent progress on the fractional Laplacian in
conformal geometry. Chapter in Recent Developments in Nonlocal
Theory. Berlin, Boston: Sciendo Migration. Palatucci, G.
& Kuusi, T. (Eds.) (2018). .pdf
- M. González, Y. Li, L. Nguyen. Existence and uniqueness to a
fully non-linear version of the Loewner-Nirenberg problem.
Commun. Math. Stat. 6 (2018), no. 3, 269–288.
.pdf
- W. Ao, H. Chan, M. González, J. Wei. Existence of
positive weak solutions for fractional Lane-Emden equations with
prescribed singular sets. Calc. Var. Partial Differential
Equations 57 (2018), no. 6, Art. 149, 25 pp.
.pdf
- C. Bandle, M. Fontelos, M. González. N. Wolanski. A nonlocal
diffusion problem on manifolds. Comm. in PDE 43 (2018), n.
4, 652-676 .pdf
- A. DelaTorre, M. González. Isolated singularities for a
semilinear equation for the fractional Laplacian arising in
conformal geometry. Rev. Mat. Iberoam. 34 (2018), no. 4,
1645–1678 .pdf
- W. Ao, H. Chan, A. DelaTorre, M. Fontelos, M. González, J.
Wei. On higher dimensional singularities for the fractional
Yamabe problem: a non-local Mazzeo-Pacard program. Duke
Math. J. Volume 168, Number 17 (2019), 3297-3411. .pdf
- W. Ao, H. Chan, M. González, J. Wei. Bound state solutions for
the supercritical fractional Schrödinger equation. Nonlinear
Analysis 193 (2020) 111448 .pdf
- W. Ao, A. DelaTorre, M. González, J. Wei. A gluing approach
for the fractional Yamabe problem with isolated singularities.
Journal für die reine und angewandte Mathematik 763 (2020),
25-78. .pdf
- S. Barbero, M.
González. Admissible surfaces in progressive addition
lenses. Optics Letters 45, n. 20, 5656-5659 (2020).
.pdf
- H. Chan, M.
González, Y. Huang, E. Mainini, B. Volzone. Uniqueness
of entire ground states for the fractional plasma problem.
Calc. Var. and PDE 59 (2020), 1-42. .pdf
- W. Ao, M. González, Y. Sire. Boundary connected sum of Escobar
manifolds. Journal of Geometric Analysis 30 (2020),
4092–4109. .pdf
- W. Ao, H. Chan,
A. DelaTorre, M. Fontelos, M. González, J. Wei. ODE-methods
in non-local equations. J. Math. Study 53 (2020), no. 4,
370–401. A special volume for Prof. A. Chang and P. Yang's
70th birthdays .pdf
- M.
González, K-A. Lee, T. Lee.
Optimal configuration and
symmetry breaking phenomena in the composite membrane
problem with fractional Laplacian. J. Differential
Equations 274 (2021), 1165–1208. .pdf
- A. DelaTorre,
M. González, A. Hyder, L. Martinazzi. Concentration
phenomena for the fractional Q-curvature equation in
dimension 3 and fractional Poisson formulas. J. Lond.
Math. Soc. (2) 104 (2021), no. 1, 423–451.
.pdf
- W. Ao, M.
González, A. Hyder, J. Wei. Removability of singularities
and superharmonicity for some fractional Laplacian
equations. Indiana Univ. Math. J. 71 (2022), no. 2, 735–766.
.pdf
- W. Ao,
A. DelaTorre, M. González. Symmetry
and symmetry breaking for the fractional
Caffarelli-Kohn-Nirenberg inequality. Journal of Functional
Analysis 282, Issue 11, 1 June 2022, 109438
.pdf
- M. González, M.
Sáez. Eigenvalue
bounds for the Paneitz operator and its associated
third-order boundary operator on locally conformally
flat manifolds. To appear in Annali della Scuola
Normale Superiore di Pisa, Classe di Scienze
.pdf
- D. Buoso, C.
Falcó, M. González, M. Miranda. Bulk-Boundary
eigenvalues for Bilaplacian problems. Discrete and
Continuous Dynamical Systems 43 (2023), no. 3-4, 1175–1200.
.pdf
- S. Barbero. M. González. Presbyopia correction, differential
geometry and free boundary PDEs. Notices Amer. Math. Soc. 70
(2023), no. 11, 1763–1771. link
- L. Brasco, M. González, M. Ispizua. A Steklov version of the
torsional rigidity. To appear in Communications in
Contemporary Mathematics .pdf
- R. Bettiol, M. González, A. Maalaoui. Multiplicity of singular
solutions to the fractional Yamabe problem on spheres. To appear
in Journal of Differential Equations .pdf
Preprints:
- E. Martínez-Enríquez, M. González, J. Portilla. Deterministic
Decoupling of Global Features and its Application to Data
Analysis .pdf
- M. González, L. Ignat, D. Manea, S. Moroianu. Concentration
limit for non-local dissipative convection-diffusion kernels on
the hyperbolic space .pdf
- M. Espinal, M. González. A gluing construction of singular
solutions for a fully non-linear equation in conformal
geometry .pdf
In preparation:
- H. Chan, M. González, R. Mazzeo. Yamabe problem with cone-edge
singularities
- H. Chan, M. Fontelos, M. González, J. Wei. Spectral properties
of Levy Fokker-Planck equations
- G. Gori, R. Graham, M. Sáez, A. Trombettoni. Geometry of
bounded critical systems
- M. González, A. Hyder, M. Sáez. The limiting case of the
fractional Caffarelli-Kohn-Nirenberg inequality.
- M. González, I. Gonzálvez, F. Quirós. Large-time behaviour of
solutions to the Fisher-KPP equation in the hyperbolic space.
- ......, joint with S. Barbero and M. Ispizua
- ................