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These lectures are an introduction to the regularity theory of minimizers of variational integrals, in the calculus of variations and of solutions of nonlinear elliptic systems. Topics covered include the Hilbert-space approach to boundary value problems and energy estimates.
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"Giaquinta...and Modica...present the differential and integral calculus for real functions of a single real variable from a sophisticated point of view. Their book is far better suited as a source of unique perspectives on the logical development of calculus ideas and their physical applications...[so that] it will better serve the experienced calculus instructor seeking new approaches to familiar material or the student who has already mastered the basic ideas and techniques of calculus but wishes to see it all again, "done right," ...Highly recommended."
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