Contemporary Research in Elliptic PDEs and Related Topics

Description

This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research. Front Matter ....Pages i-ix Getting Acquainted with the Fractional Laplacian (Nicola Abatangelo, Enrico Valdinoci)....Pages 1-105 Dirichlet Problems for Fully Nonlinear Equations with “Subquadratic” Hamiltonians (Isabeau Birindelli, Françoise Demengel, Fabiana Leoni)....Pages 107-127 Monotonicity Formulas for Static Metrics with Non-zero Cosmological Constant (Stefano Borghini, Lorenzo Mazzieri)....Pages 129-202 Introduction to Controllability of Nonlinear Systems (Ugo Boscain, Mario Sigalotti)....Pages 203-219 Introduction to Variational Methods for Viscous Ergodic Mean-Field Games with Local Coupling (Annalisa Cesaroni, Marco Cirant)....Pages 221-246 Flatness Results for Nonlocal Phase Transitions (Eleonora Cinti)....Pages 247-275 Fractional De Giorgi Classes and Applications to Nonlocal Regularity Theory (Matteo Cozzi)....Pages 277-299 Harnack and Pointwise Estimates for Degenerate or Singular Parabolic Equations (Fatma Gamze Düzgün, Sunra Mosconi, Vincenzo Vespri)....Pages 301-368 Lectures on Curvature Flow of Networks (Carlo Mantegazza, Matteo Novaga, Alessandra Pluda)....Pages 369-417 Maximum Principles at Infinity and the Ahlfors-Khas’minskii Duality: An Overview (Luciano Mari, Leandro F. Pessoa)....Pages 419-455 Singularities in the Calculus of Variations (Connor Mooney)....Pages 457-480 Comparison Among Several Planar Fisher-KPP Road-Field Systems (Andrea Tellini)....Pages 481-500