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Alberto Ferrero |
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Research interests
Elliptic problems with singular potentials
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Elliptic problems with singular potentials I focused my attention on different aspects dealing with nonlinear second order elliptic equations with singular potentials. My first paper [1] in chronological order was about a critical growth Dirichlet problem with an inverse-square potential associated with the Hardy inequality. The purpose of the paper was proving existence and multiplicity results for nontrivial solutions of the Dirichlet problem. More recently my research on singular elliptic problems mainly focused on qualitative aspects of their solutions. More precisely the main purpose of that study was to provide suitable asymptotic estimates on the behavior of solutions near the singular set of the potentials. Those results are collected in the papers [2]-[6].
[1] A. Ferrero, F. Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations,
Journal of Differential Equations 177, 2001, 494-522
[2] V. Felli, A. Ferrero, S. Terracini, Asymptotic behavior of solutions to Schrödinger equations
near an isolated singularity of the electromagnetic potential,
Journal of the European Mathematical Society 13, 2011, 119-174
[3] V. Felli, A. Ferrero, S. Terracini, On the behavior at collisions of solutions to Schrödinger
equations with many-particle and cylindrical potentials,
Discrete and Continuous Dynamical Systems, 32, 2012, 3895-3956
[4] V. Felli, A. Ferrero, S. Terracini, A note on local asymptotics of solutions to singular elliptic
equations via monotonicity methods, Milan Journal of Mathematics 80, 2012, 203-226
[5] V. Felli, A. Ferrero, Almgren-type monotonicity methods for the classification of behavior at corners of solutions
to semilinear elliptic equations, Proc. Roy. Soc. Edinburgh Sect. A 143, 2013, no. 5, 957-1019
[6] V. Felli, A. Ferrero, On semilinear elliptic equations with borderline Hardy potentials,
Journal d'Analyse Mathématique 123, 2014, no. 1, 303-340
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