Symmetry for Elliptic PDEs
About this Title
Alberto Farina and Enrico Valdinoci, Editors
This volume contains contributions from the INdAM School on Symmetry for Elliptic PDEs, which was held May 25–29, 2009, in Rome, Italy. The school marked “30 years after a conjecture of De Giorgi, and related problems” and provided an opportunity for experts to discuss the state of the art and open questions on the subject.
Motivated by the classical rigidity properties of the minimal surfaces, De Giorgi proposed the study of the one-dimensional symmetry of the monotone solutions of a semilinear, elliptic partial differential equation. Impressive advances have recently been made in this field, though many problems still remain open. Several generalizations to more complicated operators have attracted the attention of pure and applied mathematicians, both for their important theoretical problems and for their relation, among others, with the gradient theory of phase transitions and the dynamical systems.
Graduate students and research mathematicians interested in elliptic PDEs.
Table of Contents
- F. Demengel and I. Birindelli – One-dimensional symmetry for solutions of Allen Cahn fully nonlinear equations [MR 2759031]
- Ermanno Lanconelli – Maximum principles and symmetry results in sub-Riemannian settings [MR 2759032]
- Louis Dupaigne – Symétrie: si, mais seulement si? [MR 2759033]
- O. Savin – Minimal surfaces and minimizers of the Ginzburg-Landau energy [MR 2759034]
- I. E. Verbitsky – Green’s function estimates for some linear and nonlinear elliptic problems [MR 2759035]
- L. Montoro and B. Sciunzi – Monotonicity of the solutions of quasilinear elliptic equations in the half-plane with a changing sign nonlinearity [MR 2759036]
- Fausto Ferrari – Some inequalities associated with semilinear elliptic equations with variable coefficients and applications [MR 2759037]
- Louis Dupaigne and Yannick Sire – A Liouville theorem for non local elliptic equations [MR 2759038]
- Manuel del Pino, Michal Kowalczyk and Juncheng Wei – On a conjecture by De Giorgi in dimensions 9 and higher [MR 2759040]