Mariano Giaquinta 
Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105 [PDF ebook] 

A classic treatment of multiple integrals in the calculus of variations and nonlinear elliptic systems from the acclaimed Annals of Mathematics Studies series
Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century.
To mark the continued success of the series, all books are available in paperback and as ebooks.