Series:

Publications of the Scuola Normale Superiore

1 primary work • 3 total works

Book 18

Cover of Lectures on Elliptic Partial Differential Equations
The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.

Cover of Lectures on analysis in metric spaces
This book contains the notes of an international summer school on Analysis in Metric Spaces. The contributions are the following: T. Coulhon, Random walks and geometry on infinite graphs; G. David, Uniform rectifiability and quasiminimal sets; P. Koskela, Upper gradients and Poincare inequalities; S. Semmes, Derivatives and difference quotients for Lipschitz or Sobolev functions on various spaces; R. L. Wheeden, Some weighted Poincare estimates in spaces of homogenous type.

Cover of Selected topics on Analysis in Metric Spaces
These notes originated from a course given by the first author in 1998/99 in the Scuola Normale Superiore of Pisa. The aim of the course was the presentation of the main mathematical prerequisites needed for the so-called Analysis in Metric Spaces. The exposition, though not fully self contained, covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorems, Sobolev spaces; all these topics are developed in a general metric setting. We also discuss in detail the geodesic problem and the Gromov-Hausdorff convergence. The last chapter contains a brief, but very general, description of the theory of integration with respect to nondecreasing set functions.