Paolo Piovano


I received my Ph.D. in Mathematical Sciences from Carnegie Mellon University, USA in June 2012 under the supervision of Prof. Irene Fonseca and Prof. Giovanni Leoni. I am currently part of the Research Group on Applied Mathematics and Modeling at the University of Vienna.

Office: 04.131

Phone: +43 1 4277 50657
Personal eFax: +43 1 4277 850657


University of Vienna

Faculty of Mathematics

Oskar-Morgenstern-Platz 1,

1090 Wien, Austria


P.'s research area is PDEs and the Calculus of Variations, and his research program involves the investigation of Continuum and Molecular Mechanics models that find applications in Materials Science. The focus is on free boundary problems and atomistic models motivated by applications in the study of the epitaxial growth of thin films, the optimal shapes of crystal interfaces, and the stability of molecular structures.

The methodology includes configurational energy minimization, isoperimetric characterization, Gamma-convergence, and the minimizing-movement method (curriculum vitae).

Research Interests


[1] P. Piovano, Evolution and Regularity Results for Epitaxially Strained Thin Films and Material Voids, ProQuest; Thesis (Ph.D.)-Carnegie Mellon University 2012; ISBN: 9781267655349; Vol. 74-01(E), Sect. B.; p. 108. Available at and at

[2] P. Piovano, Evolution of Elastic Thin Films with Curvature Regularization via Minimizing Movements, Calc. Var. Partial Differential Equations, 49 (2014), 337-367. Preprint available at

[3] E. Mainini, P. Piovano, and U. Stefanelli, Finite Crystallization in the Square Lattice, Nonlinearity, 27 (2014), 4:717-737. See preprint.

[4] E. Mainini, P. Piovano, and U. Stefanelli, Crystalline and Isoperimetric Square Configurations, Proc. Appl. Math. Mech., 14 (2014) 1045-1048. See preprint.

[5] E. Mainini, H. Murakawa, P. Piovano, and U. Stefanelli, Carbon-nanotube Geometries: Analytical and Numerical Results, Discret. Contin. Dyn. Syst. Ser. S, 10 (2017), 141-160. See preprint.

[6] E. Davoli, P. Piovano, and U. Stefanelli, Wulff Shape Emergence in Graphene, Math. Models Methods Appl. Sci., 26-12 (2016), 2277-2310. See preprint.

[7] M. Friedrich, P. Piovano, and U. Stefanelli, The Geometry of C_60: A Rigorous Approach via Molecular Mechanics, SIAM J. Appl. Math., 76-5 (2016), 2009-2029. See preprint.

[8] E. Davoli, P. Piovano, and U. Stefanelli, Sharp N^{3/4} Law for the Minimizers of the Edge-Isoperimetric Problem on the Triangular Lattice, J. Nonlinear Sci., 27-2 (2017), 627--660. See preprint.

[9] E. Mainini, H. Murakawa, P. Piovano, and U. Stefanelli, Carbon-Nanotube Geometry as Optimal Configurations, Submitted (2016). See preprint.

[10] M. Friedrich, E. Mainini, P. Piovano, and U. Stefanelli, Characterization of optimal carbon nanotubes under stretching and validation of the Cauchy-Born rule, Submitted (2017).

[11] E. Davoli, P. Piovano, Analytical validation of the Young-Dupré law for epitaxially-strained thin films, Preprint.

[12] P. Piovano, Regularity Results for Local Minimizers of Energies Defined on Set-Function Pairs, Preprint.

- Stand-Alone Project with title Optimal Shapes of Crystal Interfaces granted by the Austrian Science Fund (FWF) for the duration of 4 years starting on September 1st, 2017 with budget of 332,262.00 Euro. Project website:

- Project awarded with title Modeling and Design of Epitaxially Strained Nanoislands and Co-PI Prof. Ulrike Diebold, Institute of Applied Physics, TU Vienna, awarded by the Vienna Science and Technology Fund (WWTF) in the framework of the 2016 Program ``Mathematics and...'' for the duration of 4 years starting on July 1st, 2017 with budget of 596,200.00 Euro (partially funded by Berndorf Foundation and the City of Vienna). Project website:

Research Projects

Taught Courses

- University of Vienna, Austria: Teaching Assistant at the Faculty of Mathematics for the following exercises courses: Partielle Differentialgleichungen (fall 2016), Analysis (spring 2016), Höhere Analysis und Differentialgeometrie (fall 2015), Analysis (spring 2015), Einführung in das mathematische Arbeiten and Einführung in die Analysis (fall 2014), Modellierung (fall 2013).

- Webster University Vienna, Austria: Lecturer for the undergraduate course College Algebra (fall 2016).

- Carnegie Mellon University, USA: Teaching Assistant at the Department of Mathematics for the following exercises courses: Calculus in Three Dimensions (spring 2011) and Differential Equations (fall 2010).

Supervised Students

Mr. Filipp Lausch, Bachelor thesis at the Department of Mathematics, University of Vienna with thesis dissertation on January 20, 2016.