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.

About the Author

Mariano Giaquinta is an Italian mathematician mainly known for his contributions to the fields of calculus of variations, regularity theory of partial differential equation. He is currently professor of mathematics at the Scuola Normale Superiore di Pisa [1] [2] and he is the director of De Giorgi center at Pisa. Luca Martinazzi is professor of mathematics at the University of Basel, Switzerland.