# Partial Differential Equations and Applications

The scientific activity of the Group is devoted to the study of equations and systems of equations of partial differential equations arising in applications, with particular reference to phase transition phenomena, dynamics of liquid crystals, population dynamics. The Group is interested in both the modeling and analytical aspects.

## Keywords

Well-posedness and regularity of solutions of nonlinear PDEs, Long-time behavior of evolution equations, Fractional Laplacian regularity theory, Fully nonlinear equations, Nonlocal equations, Inverse problems, Phase Transitions, Liquid Crystals

**Pubblications**

C. Cavaterra, E. Rocca, On a 3D isothermal model for nematic liquid crystals accounting for stretching terms, in corso di stampa su Z. Angew. Math. Phys. DOI 10.1007/s00033-012-0219-7, preprint arXiv:1107.3947v2 (2012), 1-17.

A. Farina, B. Sciunzi, E. Valdinoci, Bernstein and De Giorgi type problems: new results via a geometric approach, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 7 (2008), no. 4, 741-791.

E. Feireisl, M. Frémond, E. Rocca, G. Schimperna: A new approach to non-isothermal models for nematic liquid crystals, in corso di stampa su Archive for Rational Mechanics and Analysis, preprint arXiv:1104.1339v1 (2011), 1-21.

S. Frigeri, E. Rocca, Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D, preprint arXiv:1205.2534v1 (2012), 1-32.

O. Savin, E. Valdinoci, G -convergence for nonlocal phase transitions, Annales de l'Institut Henri Poincaré Analyse Non Linéaire (2012), no. 4, 479-500.

**Funded Projects related to the Research Theme**

PRIN 2008: Mathematical Analysis for inverse problems towards applications

PRIN: Nonlinear Elliptic Problems in the Study of Vortices and Related Topics

ERC 2011: ENTROPHASE - Entropy formulation of evolutionary phase transitions

ERC 2012: EPSILON -Elliptic Pdes and Symmetry of Interrfaces and Layers for Odd Nonlinearties

FIRB: Analysis and Beyond

## Components

Members from the Department of Mathematics | ||
---|---|---|

Cecilia CAVATERRA | info | |

Elisabetta ROCCA | info | |

Enrico VALDINOCI | info | |

Michela ELEUTERI | Post doc | info |

Sergio FRIGERI | Post doc | info |

Annalisa MASSACESI | Post doc | |

Stefania PATRIZI | Post doc since May 2013 |