Martin Fuchs

Topics in the Calculus of Variations (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book illustrates two basic principles in the calculus of variations which are the question of existence of solutions and closely related the problem of regularity of minimizers. Chapter one studies variational problems for nonquadratic energy functionals defined on suitable classes of vectorvalued functions where also nonlinear constraints are incorporated. Problems of this type arise for mappings between Riemannian manifolds or in nonlinear elasticity. Using direct methods the existence of generalized minimizers is rather easy to establish and it is then shown that regularity holds up to a set of small measure. Chapter two contains a short introduction into Geometric Measure Theory which serves as a basis for developing an existence theory for (generalized) manifolds with prescribed mean curvature form and boundary in arbitrary dimensions and codimensions. One major aspect of the book is to concentrate on techniques and to present methods which turn out to be useful for applications in regularity theorems as well as for existence problems.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Vieweg+Teubner Verlag
• Seitenzahl: 148
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783322865281
• Artikelnr.: 53390735

Autorenporträt

Prof. Dr. Martin Fuchs ist an der Universität des Saarlandes im Bereich Variationsrechnung und partielle Differentialgleichungen mit Bezügen zur mathematischen Physik und Differentialgeometrie tätig.

Inhaltsangabe

1 Degenerate Variational Integrals with Nonlinear Side Conditions, p-harmonic Maps and Related Topics.- 1.1 Introduction, Notations and Results for Minimizers.- 1.2 Linearisation of the Minimum Property, Extension of Maps.- 1.3 Proofs of the Basic Theorems.- 1.4 A Survey on p-Harmonic Maps.- 1.5 Variational Inequalities and Asymptotically Regular Integrands.- 1.6 Approximations for some Model Problems in Nonlinear Elasticity.- 2 Manifolds of Prescribed Mean Curvature in the Setting of Geometric Measure Theory.- 2.1 The Mean Curvature Problem.- 2.2 Some Facts from Geometric Measure Theory.- 2.3 A First Approach to the Mean Curvature Problem.- 2.4 General Existence Theorems, Applications to Isoperimetric Problems.- 2.5 Tangent Cones, Small Solutions, Closed Hypersurfaces.