Geometry of PDEs and Related Problems

Cetraro, Italy 2017
1. Auflage 2018
ISBN: 978-3-319-95185-0
Verlag: Springer International Publishing

Buch, Englisch, Band 2220, 198 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 330 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Cabré, Xavier

Henrot, Antoine

Peralta-Salas, Daniel

Reichel, Wolfgang

Shahgholian, Henrik

Bianchini, Chiara

Magnanini, Rolando

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

- 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.