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.

Bibliographic Information

Book Title: Convex Variational Problems
Book Subtitle: Linear, nearly Linear and Anisotropic Growth Conditions
Authors: Michael Bildhauer
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/b12308
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2003
Softcover ISBN: 978-3-540-40298-5Published: 20 June 2003
eBook ISBN: 978-3-540-44885-3Published: 01 January 2003
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XII, 220
Topics: Calculus of Variations and Optimal Control; Optimization, Partial Differential Equations

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