Dipierro S. (Ed.) Contemporary Research in Elliptic PDEs and Related Topics

Springer, 2019. — 502 p. — (Springer INdAM Series 33). — ISBN: 978-3-030-18920-4.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.Getting Acquainted with the Fractional Laplacian
Dirichlet Problems for Fully Nonlinear Equations with “Subquadratic” Hamiltonians
Monotonicity Formulas for Static Metrics with Non-zero Cosmological Constant
Introduction to Controllability of Nonlinear Systems
Introduction to Variational Methods for Viscous Ergodic Mean-Field Games with Local Coupling
Flatness Results for Nonlocal Phase Transitions
Fractional De Giorgi Classes and Applications to Nonlocal Regularity Theory
Harnack and Pointwise Estimates for Degenerate or Singular Parabolic Equations
Lectures on Curvature Flow of Networks
Maximum Principles at Infinity and the Ahlfors-Khas’minskii Duality: An Overview
Singularities in the Calculus of Variations
Comparison Among Several Planar Fisher-KPP Road-Field Systems
Tellini, Andrea