Convex Variational Problems Linear, nearly Linear and Anisotropic Growth Conditions /

• Main Author: Bildhauer, Michael (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003.
• Edition: 1st ed. 2003.
• Series: Lecture Notes in Mathematics, 1818
• Subjects: Calculus of variations.; Partial differential equations.; Calculus of Variations and Optimal Control; Optimization.; Partial Differential Equations.
• Physical Description: XII, 220 p. online resource.
• ISBN: 9783540448853
• ISSN: 0075-8434 ;
• DOI: 10.1007/b12308

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.