Bildhauer Convex Variational Problems

Linear, nearly Linear and Anisotropic Growth Conditions
Erscheinungsjahr 2003
ISBN: 978-3-540-44885-3
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 1818, 220 Seiten, eBook

Reihe: Lecture Notes in Mathematics

The author emphasizes a non-uniform ellipticity condition as the main approach to regularity theory for solutions of convex variational problems with different types of non-standard growth conditions.This volume first focuses on elliptic variational problems with linear growth conditions. Here the notion of a "solution" is not obvious and the point of view has to be changed several times in order to get some deeper insight. Then the smoothness properties of solutions to convex anisotropic variational problems with superlinear growth are studied. In spite of the fundamental differences, a non-uniform ellipticity condition serves as the main tool towards a unified view of the regularity theory for both kinds of problems.

Zielgruppe

Research

Autoren/Hrsg.

Bildhauer, Michael

Inhaltsverzeichnis

1. Introduction.- 2. Variational problems with linear growth: the general setting.- 3. Variational integrands with ($,\mu ,q$)-growth.- 4. Variational problems with linear growth: the case of $\mu $-elliptic integrands.- 5. Bounded solutions for convex variational problems with a wide range of anisotropy.- 6. Anisotropic linear/superlinear growth in the scalar case.- A. Some remarks on relaxation.- B. Some density results.- C. Brief comments on steady states of generalized Newtonian fluids.- D. Notation and conventions.- References.- Index.