Research fields
Boundary value problems for second order PDE's
Singularly and regularly perturbated problems
Potential theory and integral operators
Materials science: fractures and dislocations
Elliptic and hyperbolic PDE's in moving domains
Shape optimisation and geometric analysis
Geometric and functional inequalities
Overdetermined problems and rigidity results
Qualitative and quantitative properties for elliptic PDE's and integral identities
Coauthors
Matteo Dalla Riva, Università degli Studi di Palermo
Giuliano Lazzaroni, Università degli Studi di Firenze
Paolo Luzzini, Università degli Studi del Piemonte Orientale
Rolando Magnanini, Università degli Studi di Firenze
Paolo Musolino, Università degli Studi di Padova
Giorgio Poggesi, The University of Western Australia
Filippo Riva, Università Bocconi
Francesco Solombrino, Università degli Studi di Napoli Federico II
Publications
R. Molinarolo, Existence of solutions for a singularly perturbed nonlinear non-autonomous transmission problem, Electron. J. Differential Equations, Vol. 2019, n. 53, pp. 1-29, (2019). journal preprint
M. Dalla Riva, R. Molinarolo, P. Musolino, Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem, Nonlinear Anal. 191 (2020). journal preprint
M. Dalla Riva, R. Molinarolo, P. Musolino, Existence results for a nonlinear nonautonomous transmission problem via domain perturbation, Proc. Roy. Soc. Edinburgh Sect. A, 1-26 (2021). journal preprint
G. Lazzaroni, R. Molinarolo, F. Solombrino, Radial solutions for a dynamic debonding model in dimension two, Nonlinear Anal. 219 (2022). journal preprint
G. Lazzaroni, R. Molinarolo, F. Riva, F. Solombrino, On the wave equation on moving domains: regularity, energy balance and application to dynamic debonding, Interfaces Free Bound. 25 (2023), no. 3, pp. 401–454. journal preprint
M. Dalla Riva, P. Luzzini, R. Molinarolo, P. Musolino, Multi-parameter perturbations for the space periodic heat equation, Commun. Pure Appl. Anal. 23(2): 144-164 (2024). journal preprint
R. Magnanini, R. Molinarolo, G. Poggesi, A General Integral Identity with Applications to a Reverse Serrin Problem, J. Geom. Anal. 34, 244 (2024). journal preprint
M. Dalla Riva, P. Luzzini, R. Molinarolo, P. Musolino, Shape perturbation of a nonlinear mixed problem for the heat equation, Submitted. preprint
R. Molinarolo, Existence result for a nonlinear mixed boundary value problem for the heat equation, Submitted. preprint
Ongoing projects
M. Bonafini, V. P. Cuong Le, R. Molinarolo, Fractional semilinear wave equation on time-dependent domains.
N. Gavitone, R. Molinarolo, F. Solombrino, Anisotropic wave equation on moving domains.
N. Gavitone, R. Molinarolo, On a Serrin-type overdetemined problem with Robin boundary conditions.
R. Molinarolo, A. Roncoroni, A. Pinamonti, G. Poggesi, Alexandrov’s results on Riemannian manifolds
PhD Thesis
Riccardo Molinarolo, “Nonlinear transmission problems for the Laplace operator: a functional analytic approach”,
Supervisor: Professor Mishuris Gennady. Scientific Co-Supervisors: Professor Matteo Dalla Riva and Doctor Paolo Musolino, (2019). pdf