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. Solà-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. Communications in Contemporary Mathematics 26, No. 07, 2350037 (2024).     .pdf
  
• R. Ghinibettiol, M. González, A. Maalaoui. Multiplicity of singular solutions to the fractional Yamabe problem on spheres. J. Differential Equations 389 (2024), 285–304.   .pdf
  
• M. González, L. Ignat, D. Manea, S. Moroianu. Concentration limit for non-local dissipative convection-diffusion kernels on the hyperbolic space. To appear in Nonlinear Analysis      .pdf

Preprints:

• E. Martínez-Enríquez, M. González, J. Portilla. Deterministic Decoupling of Global Features and its Application to Data Analysis    .pdf
• M. Espinal, M. González. A gluing construction of singular solutions for a fully non-linear equation in conformal geometry      .pdf
• M. Arrayás, M. Fontelos, M. González, C. Uriarte. Evolution of vortex filaments and reconnections in the Gross-Pitaevski equation and its approximation by the binormal flow equation      .pdf
• H. Chan, M. Fontelos, M. González. Spectral properties of Levy Fokker-Planck equations    .pdf
  

In preparation:

• H. Chan, M. González, R. Mazzeo. Yamabe problem with cone-edge singularities   
  
• 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
• ................