Convex Variational Problems
Subtitle: Linear, nearly Linear and Anisotropic Growth Conditions (Lecture Notes in Mathematics)
Edition: 1 edition
Publisher: Springer
Published: August 27, 2003
Language: eng
Format: Paperback
Number of pages: 217
ISBN-13: 9783540402985
Subjects: Calculus & mathematical analysis; Mathematics; Science/Mathematics; Calculus; Differential Equations; Linear Programming; Mathematics / Linear Programming; Non-standard growth; anisotropic growth; linear growth; minimizers; regularity; General; Calculus of variations; Differential equations, Ellipt; Differential equations, Elliptic; Numerical solutions
Description: 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.