Research
Here it is a list of my scientific publications. By clicking on the title you’ll get a preprint version of the paper. While clicking on the Journal’s name you’ll be re-directed to the final published version.
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A list of my Scientific Papers:
D. Giachetti, P. J. Martínez-Aparicio, F. Murat, F. Petitta, Unexpected phenomena in a one dimensional elliptic equation with a singular first order divergence term, arXiv
D. Giachetti, F. Oliva, F. Petitta, Bounded solutions for non-parametric mean curvature problems with nonlinear terms, J. Geom. Anal., Volume 34, 265 (2024)
Antonio J. Martínez Aparicio, Francescantonio Oliva, Francesco Petitta, Optimal global BV regularity for 1-Laplace type BVP's with singular lower order terms, preprint, (2024)
F. Balducci, F. Oliva, F. Petitta, Finite energy solutions for nonlinear elliptic equations with competing gradient, singular and L^1 terms, J. Differential Equations, 391 (2024), 334-369
F. Oliva, F. Petitta, S. Segura de León, The role of absorption terms in Dirichlet problems for the prescribed mean curvature equation, Nonlinear Differential Equations and Applications, 31 (53) (2024)
J. C. Ortiz Chata, F. Petitta, Existence, non-existence and degeneracy of limit solutions to p-Laplace problems involving Hardy potentials as p-> 1, preprint 2024
L. Giacomelli, S. Moll, F. Petitta, Nonlinear Diffusion in Transparent Media, International Mathematics Research Notices, Volume 2023, Issue 4, February 2023, Pages 2944–2995
D. Giachetti, F. Oliva, F. Petitta, 1-Laplacian type problems with strongly singular nonlinearities and gradient terms, Comm. Contemp. Math., Vol. 24, No. 10, 2150081 (2022)
M. Latorre, F. Oliva, F. Petitta, S. Segura de León, The Dirichlet problem for the 1-Laplacian with a general singular term and L^1-data, Nonlinearity, 34 (2021), 1791-1816
F. Oliva, F. Petitta, A nonlinear parabolic problem with singular terms and nonregular data, Nonlinear Analysis, 194 (2020), 111472
V. De Cicco, D. Giachetti, F. Oliva, F. Petitta, The Dirichlet problem for singular elliptic equations with general nonlinearities , Calculus of Variations and Partial Differential Equations, 58: 129 (2019)
L. Giacomelli, S. Moll, F. Petitta, Nonlinear diffusion in transparent media: the resolvent equation, Adv. Calc. Var., 11 (2018), 405-432
F. Oliva, F. Petitta, Finite and Infinite energy solutions of singular elliptic problems: Existence and Uniqueness, J. Differential Equations, 264 (2018), 311-340
L. Giacomelli, S. Moll, F. Petitta, Optimal waiting time bounds for some flux-saturated diffusion equations, Comm. Partial Differential Equations, 42 (4), (2017) 556-578
F. Oliva, F. Petitta, On singular elliptic equations with measure sources, ESAIM: Control, Optimisation and Calculus of Variations, 22 (1) (2016) 289–308
A. Dall’Aglio, L. Orsina, F. Petitta, Existence of solutions for degenerate parabolic equations with singular terms, Nonlinear Analysis, 131 (2016), 273-288
F. Petitta, Some remarks on the duality method for Integro-Differential equations with measure data, Adv. Nonlinear Stud., 16 (1), (2016), 115–124
L. Orsina, F. Petitta, A lazer-Mckenna type problem with measures, Differential and Integral Equations, 29 (1-2) (2016), 19-36
F. Petitta, A. Porretta, On the notion of renormalized solution to nonlinear parabolic equations with general measure data, J. of Elliptic and Parabolic Equations, 1 (2015), 201-214
S. Moll, F. Petitta, Large solutions for the elliptic 1-Laplacian with absorption, J. Anal. Math, 125 (1) (2015), 113-138
D. Giachetti, F. Petitta, S. Segura de Leon, A priori estimates for elliptic problems with a strongly singular gradient term and a general datum, Differential and Integral Equations, 26 (9/10) (2013), 913-948
D. Blanchard, F. Petitta, H. Redwane, Renormalized solutions of nonlinear parabolic equations with diffuse measure data, Manuscripta Mathematica, 141, (2013), 601–635
D. Giachetti, F. Petitta, S. Segura de Leon, Elliptic equations having a singular quadratic gradient term and a changing sign datum, Comm. Pure and Appl. Anal., 11 (5), (2012) 1875–1895
S. Moll, F. Petitta, Large solutions for nonlinear parabolic problems without absorption terms, J. Functional Analysis, 262 (2012) 1566–1602
F. Petitta, A. Ponce and A. Porretta, Diffuse measures and nonlinear parabolic equations, J. Evol. Equations, 11 (4) (2011), 861-905
T. Leonori, F. Petitta, Local estimates for parabolic equations with nonlinear gradient terms, Calc. Var. and Partial Differential Equations, 42 (2011) 153-187
L. Boccardo, T. Leonori, L. Orsina, F. Petitta, Quasilinear elliptic equations with singular absorption terms, Commun. Contemp. Math., 13 No. 4 (2011) , 607–642
P. J. Martínez-Aparicio, F. Petitta, Parabolic equations with nonlinear singularities, Nonlinear Analysis, 74 (2011) 114-131
K. H. Karlsen, F. Petitta, S. Ulusoy, A duality approach to the fractional laplacian with measure data, Publ. Mat., 55 (2011), 151-161
F. Petitta, A generalized porous medium equation related to some singular quasilinear problems, Nonlinear Analysis, 72 (2010) 4115-4123
D. Arcoya, J. Carmona, T. Leonori, P. J. Martínez-Aparicio, L. Orsina, F. Petitta, Existence and Nonexistence Results for Singular Quasilinear Equations, J. Differential Equations 246 (10), (2009) 4006–4042
F. Petitta, A nonexistence result for nonlinear parabolic equations with singular measure data, Proc. Roy. Soc. Edinburgh A, 139 (2), (2009), 381–392
F. Petitta, A. C. Ponce, A. Porretta, Approximation of diffuse measures for parabolic capacities, C. R. Acad. Sci. Paris, Ser. I 346 (2008), 161– 166
F. Petitta, Renormalized solutions of nonlinear parabolic equations with general measure data, Ann. Mat. Pura ed Appl., 187 (4) (2008), 563– 604
F. Petitta, Large time behavior for solutions of nonlinear parabolic problems with sign-changing measure data, Electron. J. Differential Equations, 132 (2008), 1–10
F. Petitta, Asymptotic behavior of solutions for parabolic operators of Leray–Lions type and measure data, Adv. Differential Equations 12 (2007), no. 8, 867–891
T. Leonori, F. Petitta, Existence and regularity results for some singular elliptic problems, Adv. Nonlinear Stud., 7 (2007), n. 3, 329–344
F. Petitta, Asymptotic behavior of solutions for linear parabolic equations with general measure data, C. R. Acad. Sci. Paris, Ser. I 344 (2007) 571–576
F. Petitta, Equazioni paraboliche nonlineari con dato misura, Boll. Unione Mat. Ital. Sez. A 2, (2007), 323–326
T. Leonori, F. Petitta, Asymptotic behavior for solutions of parabolic equations with natural growth terms and irregular data, Asymptotic Analysis 48(3) (2006), 219–233
Proceedings and Congress Acta
Giachetti, P. Donato, F. Petitta, S. Segura de Leon, Singular problems: existence and homogenization results, Actes du colloque Edp- Normandie. Le Havre 2012. 61–67. FNM Federation Normandie Mathematiques, 2013 Paris, France
S. Moll, F. Petitta, Large Solutions for Parabolic Equations Without Absorption, Proceedings XXII Congreso de Ecuaciones Diferenciales y Aplicaciones, XII Congreso de Matematica Aplicada, Universidad de Les Illes Balears, Palma de Mallorca, (September 5–9, 2011), (Actas Electronicas). ISBN: 978-84-694-4935-6
F. Petitta, A. C. Ponce, A. Porretta, Nonlinear parabolic equations with absorption terms and measure data, Proceedings XXII Congreso de Ecuaciones Diferenciales y Aplicaciones, XII Congreso de Matematica Aplicada, Universidad de Les Illes Balears, Palma de Mallorca, (September 5–9, 2011), (Actas Electronicas). ISBN: 978-84-694-4935-6
Lecture Notes and Technical Reports
F. Petitta, D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order. (Book review), SIAM Rev. 61, No. 4, 903-906 (2019).
F. Petitta, A Not So Long Introduction to the Weak Theory of Parabolic Equations with Singular Data, Lecture Notes of the Facultad de Ciencias, Universidad de Granada (Spain), October-December 2007.
F. Petitta, Nonlinear parabolic equations with general measure data, Ph. D. Thesis (2006).
F. Petitta, Soluzioni rinormalizzate per equazioni ellittiche con dati misura, Master Thesis (2001), (Advisor: Prof. Luigi Orsina)