Personal page of Enea Parini

Enea Parini

Assistant Professor in Applied Mathematics

Institut de Mathématiques de Marseille
Aix-Marseille Université

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List of publications

Research publications in peer-reviewed international journals

[1] C. Grumiau, E. Parini, On the asymptotics of solutions of the Lane-Emden problem for the $p$-Laplacian, Arch. Math. 91 (2008), 354-365.

[2] E. Parini, A. Stylianou, On the positivity preserving property of hinged plates, SIAM J. Math. Anal. 41 (2009), 2031-2037.

[3] E. Parini, The second eigenvalue of the p-Laplacian as p goes to 1, Int. J. Differ. Equ. (2010), Article ID 984671, 23 pp.

[4] F. Charro, E. Parini, Limits as $p\to\infty$ of $p$-Laplacian problems with a superdiffusive power-like nonlinearity: positive and sign-changing solutions, J. Math. Anal. Appl. 372 (2010), 629-644.

[5] E. Parini, Continuity of the variational eigenvalues of the p-Laplacian with respect to p, Bull. Aust. Math. Soc. 83(2011), 376-381.

[6] F. Charro, E. Parini, Limits as $p \to \infty$ of p-laplacian eigenvalue problems perturbed with a concave or convex term , Calc. Var. Partial Differential Equations 6 (2013), 403-425.

[7] E. Parini, B. Ruf, C. Tarsi, The eigenvalue problem for the 1-biharmonic operator, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 13 (2014), 307-332.

[8] E. Parini, N. Saintier, Shape derivative of the Cheeger constant, ESAIM Control Optim. Calc. Var. 21 (2015), no. 2, 348-358.

[9] E. Parini, B. Ruf, C. Tarsi, Higher-order functional inequalities related to the 1-biharmonic operator, Ann. Mat. Pura Appl. (4) 194 (2015), no. 6, 1835-1858.

[10] L. Brasco, E. Lindgren, E. Parini, The fractional Cheeger problem, Interfaces Free Bound. 16 (2014), 419-458.

[11] F. Charro, E. Parini, On the existence threshold for positive solutions of p-laplacian equations with a concave-convex nonlinearity, Commun. Contemp. Math. 17 (2015).

[12] E. Parini, T. Weth, Existence, unique continuation and symmetry of least energy nodal solutions to sublinear Neumann problems, Math. Z. 280 (2015), 707-732.

[13] E. Parini, Reverse Cheeger inequality for planar convex sets, J. Convex Anal. 24 (2017), no. 1, 107–122.

[14] L. Brasco, E. Parini, The second eigenvalue of the fractional p-Laplacian, Adv. Calc. Var. 9 (2016), no. 4, 323--355.

[15] L. Brasco, E. Parini, M. Squassina, Stability of variational eigenvalues for the fractional p-Laplacian, Discrete Contin. Dyn. Syst. 36 (2016), no. 4, 1813-1845

[16] N. Katzourakis, E. Parini, The eigenvalue problem for the $\infty$-bilaplacian, NoDEA Nonlinear Differential Equations Appl. 24 (2017), no. 6, art. 32, 18 pp.

[17] B. Audoux, V. Bobkov, E. Parini, On multiplicity of eigenvalues and symmetry of eigenfunctions of the $p$-Laplacian, Topol. Methods Nonlinear Anal. 51, no. 2 (2018), 565-582.

[18] E. Parini, A. Stylianou, A free boundary approach to the Rosensweig instability of ferrofluids, Z. Angew. Math. Phys. 69 (2018), no. 2, art. 32, 18 pp.

[19] V. Bobkov, E. Parini, On the higher Cheeger problem, J. Lond. Math. Soc. 97 (2018), no. 3, 575-600.

[20] E. Parini, B. Ruf, On the fractional Moser-Trudinger inequality in Sobolev-Slobodeckij spaces, J. Anal. Math. 138 (2019), no. 1, 281-300.

[21] E. Parini, A. Salort, Compactness and dichotomy in nonlocal shape optimization, Math. Nachr. 293 (2020) 2208--2232.

[22] D. Buoso, E. Parini, The buckling eigenvalue problem in the annulus, Commun. Contemp. Math. 23 (2021), no. 4, Paper No. 2050044, 19 pp.

[23] V. Bobkov, E. Parini, On the Cheeger problem for rotationally invariant domains, Manuscripta Math. 166 (2021), 503--522.

[24] E. Parini, A. Salort, J. D. Rossi, Reverse Faber-Krahn inequality for a truncated laplacian operator, Publ. Math. 66 (2) (2022), 441--455.

[25] D. Bonheure, E. Moreira dos Santos, E. Parini, H. Tavares, T. Weth, Nodal solutions for sublinear-type problems with Dirichlet boundary conditions, Int. Math. Res. Not. IMRN 2022 (5) (2022), 3760--3804.

[26] E. Parini, G. Saracco, Optimization of the anisotropic Cheeger constant with respect to the anisotropy, Canad. Math. Bull. 66 (3) (2023), 1030--1043.

[27] A. DelaTorre, E. Parini, Uniqueness of least energy solutions of the fractional Lane-Emden equation in the ball, submitted.

Research publications in conference proceedings

[1] E. Parini, On the Lane-Emden problem for the p-Laplacian, Oberwolfach reports 6 (2009), 1457-1459.

[2] E. Parini, Positivity preserving property for the hinged plate, Oberwolfach reports 7 (2010), 335-336.

[3] E. Parini, B. Ruf, C. Tarsi, Limiting Sobolev inequalities and the 1-biharmonic operator, Adv. Nonlinear Anal. 3 S1 (2014), s19-s36.

[4] E. Parini, B. Ruf, On the fractional Moser-Trudinger inequality in Sobolev-Slobodeckij spaces, Rend. Lincei Mat. Appl. 29 (2018), 315-319.

Other publications (peer-reviewed)

[1] E. Parini, An introduction to the Cheeger problem, Surv. Math. Appl. 6 (2011), 9-22.

Last modified: 15/11/2023