Cartesian Currents in the Calculus of Variations I: Cartesian Currents

ISBN-13: 9783642083747 / Angielski / Miękka / 2010 / 711 str.

Mariano Giaquinta; Giuseppe Modica; Jiri Soucek

Opis

This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph

Recenzje

"Bei dieser Monographie handelt es sich um einen Bericht von der vordersten Forschungsfront, der gleichzeitig jedem an dieser Art von Problemen interessierten Mathematiker zugänglich ist. Das ist ein seltener Glücksfall, für den man den Autoren gar nicht genug danken kann. Wer sich durch den schieren Umfang der beiden Bände nicht abschrecken lässt, wird diese, einmal zur Hand genommen, nicht so schnell wieder ins Regal zurückstellen wollen.
DMV Jahresbericht Bd. 103, Heft 1, 2001

Spis treści

Part I: General Measure Theory.- Integer Rectifiable Currents.- Cartesian Maps.- Cartesian Currents in Euclidean Spaces.- Cartesian Currents in Riemannian Manifolds.- Part II: Regular Variational Integrals.- Finite Elasticity and Weak Diffeomorphisms.- The Dirichlet Integral in Sobolev Spaces.- The Dirichlet Energy for Maps into S2.- Regular and Non Regular Integrals.- The Non Parametric Area Functional.