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Alberto Ferrero |
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Research interests
Higher order equations
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Higher order equations A wide part of my research was devoted to the study of higher order equations especially with the biharmonic operator. Several aspects were considered like qualitative behavior of solutions (see [2],[5],[7],[8]), symmetry properties of solutions (see [3]), nonstandard boundary conditions and shape optimization problems for related eigenvalue problems (see [1],[6]), stability properties of entire solutions (see [9],[10]). Finally one of the papers (see [4]) is devoted to a nonlinear evolution problem with the "biharmonic" heat operator; sign properties and asymptotic estimates are provided for the corresponding solutions.
[1] A. Ferrero, F. Gazzola, T. Weth, On a fourth order Stekloff eigenvalue problem,
Analysis 25, 2005, 315-332
[2] A. Ferrero, H.C. Grunau, The Dirichlet problem for supercritical biharmonic equations with power-type
nonlinearity, Journal of Differential Equations 234, 2007, 582-606
[3] A. Ferrero, F. Gazzola, T. Weth, Positivity, Symmetry and uniqueness for minimizers of second order
Sobolev inequalities, Annali di Matematica Pura e Applicata 186, n. 4, 2007, 565-578
[4] A. Ferrero, F. Gazzola, H.-Ch. Grunau, Decay and eventual local positivity for biharmonic parabolic equations,
Discrete and Continuous Dynamical Systems and Applications 21, n. 4, 2008, 1129-1157
[5] A. Ferrero, H.-Ch. Grunau, P. Karageorgis, Supercritical biharmonic equations with power-type
nonlinearity, Annali di Matematica Pura e Applicata 188, n. 1, 2009, 171-185
[6] D. Bucur, A. Ferrero, F. Gazzola, On the first eigenvalue of a fourth order Steklov problem,
Calculus of Variations and Partial Differential Equations 35, 2009, 103-131
[7] A. Ferrero, G. Warnault, On solutions of second and fourth order elliptic equations with
power-type nonlinearities, Nonlinear Analysis 70, 2009, 2889-2902
[8] E. Berchio, A. Ferrero, F. Gazzola, P. Karageorgis, Qualitative behavior of global solutions to
some nonlinear fourth order differential equations, Journal of Differential Equations 251, 2011, 2696-2727
[9] E. Berchio, A. Farina, A. Ferrero, F. Gazzola, Existence and stability of entire solutions to a semilinear
fourth order elliptic problem, Journal of Differential Equations 252, 2012, 2596-2616
[10] A. Farina, A. Ferrero, Existence and stability properties of entire solutions to the polyharmonic equation
$(-\Delta)^m u=e^u$ for any $m\ge 1$,
online publication on Annales de l'Institut Henri Poincaré (C) Non Linear Analysis
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