Shape optimization and spectral theory

Henrot, Antoine

De Gruyter Open

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.

Geometry of PDEs and Related Problems: Cetraro, Italy 2017 (C.I.M.E. Foundation Subseries)

Cabré, Xavier

Peralta-Salas, Daniel

Reichel, Wolfgang

Shahgholian, Henrik

Reference

Springer

<p>This book focuses on extremal problems. For instance, it seeks a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. Also considered is the case of functions of eigenvalues. The text probes similar questions for other elliptic operators, such as Schrodinger, and explores optimal composites and optimal insulation problems in terms of eigenvalues.</p>

Extremum Problems for Eigenvalues of Elliptic Operators (Frontiers in Mathematics)

Science & Math

Mathematics

Birkhauser

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