Geometry of PDEs and Related Problems - Cetraro, Italy 2017

The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references.
Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19-23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.

List of contents

- Stable Solutions to Some Elliptic Problems: Minimal Cones, the Allen-Cahn Equation, and Blow-Up Solutions. - Isoperimetric Inequalities for Eigenvalues of the Laplacian. - Topological Aspects of Critical Points and Level Sets in Elliptic PDEs. - Symmetry Properties for Solutions of Higher-Order Elliptic Boundary Value Problems. - Recent Trends in Free Boundary Regularity.

Summary

The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references.Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.

Product details

• Authors: Xavie Cabré, Xavier Cabré, Antoin Henrot, Antoine Henrot, Danie Peralta-Salas, Daniel Peralta-Salas, Wolfgang Reichel, Henrik Shahgholian
• Assisted by: Chiara Bianchini (Editor), Antoin Henrot (Editor), Antoine Henrot (Editor), Rolando Magnanini (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2018
• EAN: 9783319951850
• ISBN: 978-3-31-995185-0
• No. of pages: 198
• Dimensions: 155 mm x 14 mm x 234 mm
• Weight: 330 g
• Illustrations: XI, 198 p. 35 illus., 4 illus. in color.
• Series: Lecture Notes in Mathematics; C.I.M.E. Foundation Subseries; Lecture Notes in Mathematics; C.I.M.E. Foundation Subseries
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; Analysis, B, Dynamics, Mathematics and Statistics, Functional Analysis, Dynamical Systems and Ergodic Theory, Partial Differential Equations, Ergodic theory, Nonlinear science, Dynamical systems, Stochastics, Functional analysis & transforms, Potential Theory, Potential theory (Mathematics)