---

＜電子ブック＞
Convex Variational Problems : Linear, nearly Linear and Anisotropic Growth Conditions / by Michael Bildhauer
(Lecture Notes in Mathematics. ISSN:16179692 ; 1818)

版	1st ed. 2003.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2003
本文言語	英語
大きさ	XII, 220 p : online resource
著者標目	*Bildhauer, Michael author SpringerLink (Online service)
件　名	LCSH:Mathematical optimization LCSH:Calculus of variations LCSH:Differential equations FREE:Calculus of Variations and Optimization FREE:Differential Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/b12308

 類似資料