An Introduction to the Regularity Theory for Elliptic Systems, Harmonic Maps and Minimal Graphs

• Main Authors: Giaquinta, Mariano (Author), Martinazzi, Luca (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale, 2012.
• Series: Publications of the Scuola Normale Superiore
• Subjects: Mathematics.; Partial differential equations.; Partial Differential Equations.

This volume deals with the regularity theory for elliptic systems. We may find the origin of such a theory in two of the problems posed by David Hilbert in his celebrated lecture delivered during the International Congress of Mathematicians in 1900 in Paris: 19th problem: Are the solutions to regula...

Table of Contents:

• 1 Harmonic functions
• 2 Direct methods
• 3 Hilbert space methods
• 4 L2-regularity: the Caccioppoli inequality
• 5 Schauder estimates
• 6 Some real analysis
• 7 Lp-theory
• 8 The regularity problem in the scalar case
• 9 Partial regularity in the vector-valued case
• 10 Harmonic maps
• 11 A survey of minimal graphs.