Cartesian Currents in the Calculus of Variations I

Cartesian Currents
1998
ISBN: 978-3-540-64009-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 37, 711 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1262 g

Reihe: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

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

Zielgruppe

Research

Autoren/Hrsg.

Giaquinta, Mariano

Soucek, Jiri

Modica, Giuseppe

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung

Inhaltsverzeichnis

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.