Pierpaolo
Soravia
Professor
Dipartimento di
Matematica "Tullio Levi Civita"
Università degli Studi di
Padova (Padua, Italy)
Torre Archimede, Office 5BC16
Contacts: Voice +39(0)49-827-1496
Email soravia "AT" math.unipd.it
Degree in Mathematics: University of Padova, 1981–1986.
Ph.D. in Mathematics: Universities of Bologna and Padova, 1987–1991.
Research Associate (1990–98), tenured in 1993.
Associate Professor (1998–2001), Full Professor (2001–present).
Visiting researcher: Brown University, UC Santa Barbara, Carnegie Mellon University, Australian National University.
Find me on:
ResearchGate,
Orcid,
Google scholar
I have been invited to give lectures in:
Bressanone, Canberra, Cortona, Heraklion, Irsee, Levico Terme,
Madison, Minneapolis, New York, Orleans, Paris, Pisa, Pittsburgh,
Providence, Raleigh, Roma, Salice Terme, San Diego, Santa
Barbara, Siena, Sofia, St Louis, Sydney, Tokyo, Torino, Trieste, Urawa, Valparaiso, Vancouver
- Nonlinear partial differential equations: Hamilton-Jacobi equations and viscosity solutions, Aronsson equation.
- Mathematical control theory: nonlinear optimal control, controllability, differential games, and nonsmooth analysis.
- Multiscale problems in nonlinear PDEs.
- Calculus of variations: geometric flows, minimization in L-infinity.
Selected Publications (full
list)
- Soravia, Pierpaolo \emph{Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex Hamiltonians.} Comm. Partial Differential Equations 18 (1993), no. 9-10, 1493-1514.
- Soravia, Pierpaolo \emph{$\mathcal H_\infty$ control of nonlinear systems: differential games and viscosity solutions. SIAM J. Control Optim.} 34 (1996), no. 3, 1071-1097.
- Crandall, M. G.; Kocan, M.; Soravia, P.; Swiech, A. \emph{On the equivalence of various weak notions of solutions of elliptic PDEs with measurable ingredients.} Progress in elliptic and parabolic partial differential equations (Capri, 1994), 136-162, Pitman Res. Notes Math. Ser., 350, Longman, Harlow, 1996.
- Bardi, Martino; Falcone, Maurizio; Soravia, Pierpaolo \emph{Numerical methods for pursuit-evasion games via viscosity solutions.} Stochastic and differential games, 105-175, Ann. Internat. Soc. Dynam. Games, 4, Birkhauser Boston, Boston, MA, 1999.
- Soravia, Pierpaolo \emph{Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian.} Indiana Univ. Math. J. 51 (2002), no. 2, 451-477.
- Soravia, Pierpaolo \emph{Generalized motion of a front propagating along its normal direction: a differential games approach.} Nonlinear Anal. 22 (1994), no. 10, 1247-1262.
- Soravia, Pierpaolo \emph{Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. II. Equations of control problems with state constraints.} Differential Integral Equations 12 (1999), no. 2, 275-293.
- Soravia, Pierpaolo \emph{Pursuit-evasion problems and viscosity solutions of Isaacs equations.} SIAM J. Control Optim. 31 (1993), no. 3, 604-623.
- Soravia, Pierpaolo \emph{Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. I. Equations of unbounded and degenerate control problems without uniqueness.} Adv. Differential Equations 4 (1999), no. 2, 275-296.
- Bardi, Martino; Soravia, Pierpaolo \emph{Hamilton-Jacobi equations with singular boundary conditions on a free boundary and applications to differential games.} Trans. Amer. Math. Soc. 325 (1991), no. 1, 205-229.
-
P. Soravia and P.~E. Souganidis, Phase-field theory for FitzHugh-Nagumo-type systems, SIAM J. Math. Anal. {\bf 27} (1996), no.~5, 1341--1359;
Recent publications and preprints
(on Arxiv)
-
M. Costantini, P. Soravia, On the optimal second order decrease rate for nonlinear and symmetric control systems, (2024), AIMS Mathematics, Volume 9, Issue 10: 28232-28255; (open access). doi: https://www.doi.org/10.3934/math.20241369.(abstract
available)
-
P. Soravia, A Hamiltonian approach to small time local attainability of manifolds for nonlinear control systems, Appl. Math. Optim. {\bf 88} (2023), no.~1, Paper No. 1, 39 pp.; (open access)
-
M. Bardi, E. Feleqi and P. Soravia, Regularity of the minimum time and of viscosity solutions of degenerate eikonal equations via generalized Lie brackets, Set-Valued Var. Anal. {\bf 29} (2021), no.~1, 83--108;
-
P. Soravia, A degenerate elliptic equation for second order controllability of nonlinear systems, Minimax Theory Appl. {\bf 5} (2020), no.~2, 413--437;
-
C. De~Zan and P. Soravia, Singular limits of reaction diffusion equations and geometric flows with discontinuous velocity, Nonlinear Anal. {\bf 200} (2020), 111989, 24 pp.;
-
C. De~Zan and P. Soravia, On viscosity and equivalent notions of solutions for anisotropic geometric equations, Abstr. Appl. Anal. {\bf 2020}, Art. ID 7545983, 14 pp.; (open access)
-
P. Soravia, The Aronsson equation, Lyapunov functions, and local Lipschitz regularity of the minimum time function, Abstr. Appl. Anal. {\bf 2019}, Art. ID 6417074, 9 pp., (open access)
-
Soravia, Pierpaolo, Some Results on Second Order Controllability Conditions, (2019), in {I58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, December 11-13, 2019. IEEE)}, pp. 1468-1473
Universita`
di Padova Home Page
Last
Modified 08/31/24