Publications List

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/	Authors	Title	Preprint	Journal
54	Bonforte M., Fuertes-Moran C.	Sharp Boundary Estimates and Harnack Inequalities for Fractional Porous Medium type Equations	arXiv.org	Preprint (2025)
53	Barbieri D. Bonforte M., Ibarrondo P.	Is Stochastic Gradient Descent Effective? A PDE Perspective on Machine Learning processes	arXiv.org	Preprint (2025)
52	Bonforte M., Maggi F. Restrepo D.	Asymptotic behavior of a diffused interface volume-preserving mean curvature flow	arXiv.org	Preprint (2024)
51	Bonforte M., Chlebicka I., Simonov N.	Refined asymptotics for the Cauchy problem for the fast p-Laplace evolution equation	arXiv.org	Preprint (2024)
50	Bonforte M., Salort A.	Sharp regularity estimates for 0-order p-Laplacian evolution problems	arXiv.org	Preprint (2024)
49	Berchio E., Bonforte M., Grillo G.	Smoothing effects and extinction in finite time for fractional fast diffusions on Riemannian manifolds	arXiv.org	J. Geom. Anal. (2025)
48	Bonforte M., Gualdani M., Ibarrondo P.,	Time-Fractional Porous Medium Type Equations. Sharp Time Decay and Regularization	arXiv.org	Preprint (2024)
47	Bonforte M., Figalli, A.	The Cauchy-Dirichlet Problem for the Fast Diffusion Equation on Bounded Domains	arXiv.org	Nonlin. Anal. (2024)
46	Bonforte M., Endal J.	Nonlocal Nonlinear Diffusion Equations. Smoothing Effects, Green Functions, and Functional Inequalities	arXiv.org	J. Funct. Anal. (2023)
45	Bonforte M., Ibarrondo P., Ispizua M.	The Cauchy-Dirichlet Problem for Singular Nonlocal Diffusions on Bounded Domains	arXiv.org	Discr. Cont. Dyn. Sys. (2022)
44	Bonforte M., Dolbeault J., Nazaret B. Simonov N.	Constructive stability results in interpolation inequalities and explicit improvements of decay rates of fast diffusion equations	arXiv.org	Discr. Cont. Dyn. Sys. (2022)
43	Berchio E., Bonforte M., Grillo G. Muratori M.,	The Fractional Porous Medium Equation on noncompact Riemannian manifolds	arXiv.org	Math. Ann. (2024)
42	Bonforte M., Dolbeault J., Nazaret B. Simonov N.	Stability in Gagliardo-Nirenberg-Sobolev inequalities: flows, regularity and the entropy method	arXiv.org	Memoirs AMS (2025)
41	Bonforte M., Stan D. Simonov N.	The Cauchy problem for the fast p-Laplacian evolution equation. Characterization of the global Harnack principle and fine asymptotic behaviour.	arXiv.org	J. Math. Pure Appl. (2022)
40	Bonforte M., Dolbeault J., Nazaret B. Simonov N.	Stability in Gagliardo-Nirenberg inequalities	arXiv.org HAL	Preprint (2020)
39	Bonforte M., Dolbeault J., Nazaret B. Simonov N.	Stability in Gagliardo-Nirenberg inequalities - Supplementary material: Explicit constants in Harnack inequalities and regularity estimates, with an application to the fast diffusion equation	arXiv.org HAL	Preprint (2020)
38	Berchio E., Bonforte M., Ganguly D., Grillo G.	The Fractional Porous Medium Equation on the hyperbolic space	arXiv.org	Calc. Var. PDEs (2020)
37	Bonforte M., Simonov N.	Fine properties of solutions to the Cauchy problem for a Fast Diffusion Equation with Caffarelli-Kohn-Nirenberg weights	arXiv.org	Ann. Inst. H. Poinc. (2022)
36	Bonforte M., Figalli, A.	Sharp Extinction Rates for Fast Diffusion Equations on Generic Bounded Domains	arXiv.org	Comm. Pure Appl. Math. (2021)
35	Bonforte M., Simonov N.	Quantitative a Priori Estimates for Fast Diffusion Equations with Caffarelli-Kohn-Nirenberg weights. Harnack inequalities and Hölder continuity	arXiv.org	Advances in Math. (2019)
34	Bonforte M., Figalli, A. Vázquez J. L.	Sharp boundary behaviour of solutions to semilinear nonlocal elliptic equations	arXiv.org	Calc. Var. PDEs (2018)
33	Bonforte M., Figalli, A. Vázquez J. L.	Sharp global estimates for local and nonlocal porous medium-type equations in bounded domains	arXiv.org	Analysis & PDE (2018)
32	Bonforte M., Sire Y., Vázquez J. L.	Optimal Existence and Uniqueness Theory for the Fractional Heat Equation	arXiv.org	Nonlin. Anal. TMA (2017)
31	Bonforte M., Dolbeault J., Muratori M., Nazaret B.	Weighted fast diffusion equations (Part II): Sharp asymptotic rates of convergence in relative error by entropy methods	arXiv.org	Kinet. Rel. Mod. (2017)
30	Bonforte M., Dolbeault J., Muratori M., Nazaret B.	Weighted fast diffusion equations (Part I): Sharp asymptotic rates without symmetry and symmetry breaking in Caffarelli-Kohn-Nirenberg inequalities	arXiv.org	Kinet. Rel. Mod. (2017)
29	Bonforte M., Figalli, A. Ros-Oton, X.	Infinite speed of propagation and regularity of solutions to the fractional porous medium equation in general domains	arXiv.org	Comm. Pure Appl. Math. (2017)
28	Bonforte M., Caffarelli L. A. Grillo G.,	Foreword. Nonlinear Partial Differential Equations, in honor of Juan Luis Vázquez for his 70th birthday	Volume 2	(Guest Editor) Nonlin. Anal. TMA (2016)
27	Bonforte M., Caffarelli L. A. Grillo G.,	Foreword. Nonlinear Partial Differential Equations, in honor of Juan Luis Vázquez for his 70th birthday	Volume 1	(Guest Editor) Nonlin. Anal. TMA (2016)
26	Bonforte M., Segatti A., Vázquez J. L.	Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations	arXiv.org	Calc. Var. PDEs (2016)
25	Bonforte M., Vázquez J. L.	Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains part I. Existence, Uniqueness and Upper Bounds	arXiv.org	Nonlin. Anal. TMA (2016)
24	Bonforte M., Sire Y., Vázquez J. L.	Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains	arXiv.org	Discr. Cont. Dyn. Sys. (2015)
23	Bonforte M., Vázquez J. L.	A Priori Estimates for Fractional Nonlinear Degenerate Diffusion Equations on bounded domains	arXiv.org	Arch. Rat. Mech. Anal. (2015)
22	Bonforte M., Di Castro A.,	Quantitative local estimates for nonlinear elliptic equations involving p-Laplacian type operators		Riv. Mat. Univ. Parma (2014)
21	Bonforte M., Vázquez J. L.	Quantitative Local and Global A Priori Estimates for Fractional Nonlinear Diffusion Equations	arXiv.org	Advances in Math. (2014)
20	Bonforte M., Grillo G., Vázquez J. L.	Quantitative Bounds for Subcritical Semilinear Elliptic Equations		Contemp. Math. (2013)
19	Bonforte M., Grillo G., Vázquez J. L.	Quantitative Local Bounds for Subcritical Semilinear Elliptic Equations	arXiv.org	Milan J. Math (2012)
18	Bonforte M., Figalli, A.	Total Variation Flow and Sign Fast Diffusion in one dimension	arXiv.org	J. Diff. Eq. (2012)
17	Bonforte M., Gazzola F., Grillo G., Vázquez J. L.	Classification of radial solutions to the Emden-Fowler equation on the hyperbolic space	arXiv.org	Calc. Var. PDE (2013)
16	Bonforte M., Grillo G., Vázquez J. L.	Behaviour near extinction for the Fast Diffusion Equation on bounded domains	arXiv.org	J. Math. Pure Appl. (2012)
15	Bonforte M., Dolbeault J., Grillo G., Vázquez J. L.	Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities	arXiv.org	Proc. Nat. Acad. of Science (2010)
14	Bonforte M., Iagar R.G., Vázquez J. L.	Local smoothing effects, positivity, and Harnack inequalities for the fast p-Laplacian equation	arXiv.org	Advances in Math. (2010)
13	Bonforte M., Vázquez J. L.	Positivity, local smoothing and Harnack inequalities for very fast diffusion equations	arXiv.org	Advances in Math. (2010)
12	Bonforte M., Grillo G., Vázquez J. L.	Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold	arXiv.org	Arch. Rat. Mech. Anal. (2010)
11	Blanchet A., Bonforte M., Dolbeault J., Grillo G., Vázquez J. L.	Asymptotics of the fast diffusion equation via entropy estimates	arXiv.org	Arch. Rat. Mech. Anal. (2009)
10	Bonforte M., Grillo G., Vázquez J. L.	Fast diffusion flow on manifolds of nonpositive curvature		J. Evol. Equ. (2008)
9	Blanchet A., Bonforte M., Dolbeault J., Grillo G., Vázquez J. L.	Hardy-Poincaré inequalities and applications to nonlinear diffusions		C. R. Math. Acad. Sci. Paris (2007)
8	Bonforte M., Grillo G.,	Singular evolution on manifolds, their smoothing properties, and Sobolev inequalities		Discr. and Cont. Dyn. Sys. (2007)
7	Bonforte M., Vázquez J. L.	Reverse Smoothing Effects, Fine Asymptotics and Harnack Inequalities for Fast Diffusion Equations		Bound. Val. Probl. (2007)
6	Bonforte M., Vázquez J. L.	Global positivity estimates and Harnack inequalities for the fast diffusion equation		J. Funct. Anal. (2006)
5	Bonforte M., Grillo G.,	Super and ultracontractive bounds for doubly nonlinear evolution equations		Rev. Mat. Iberoam. (2006)
4	Bonforte M., Grillo G.,	Asymptotics of the porous media equation via Sobolev inequalities		J. Funct. Anal. (2005)
3	Bonforte M., Grillo G.,	Direct and reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities		Bull. Polish Acad. Sci. Math. (2005)
2	Bonforte M., Grillo G.,	Ultracontractive bounds for nonlinear evolution equations governed by the subcritical p-Laplacian		Book Chapter Birkhäuser Basel (2005)
1	Bonforte M., Cipriani F., Grillo G.,	Ultracontractivity and Convergence to Equilibrium for Supercritical Quasilinear Parabolic Equations on Riemannian Manifolds		Adv. in Diff. Eq. (2003)

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Publications List