Sobolev classes over infinite-dimensional spaces with measures

Vladimir Bogachev

(Moscow State University, Russia)

Event: ERC School on Geometric Measure Theory and Real Analysis

Date: Sep 30, 2013

Place: Centro De Giorgi

Abstract. This mini-course aims at giving a concise introduction to the theory of Sobolev classes over infinite-dimensional spaces with measures. The framework is a natural generalization of the finite-dimensional case of weighted Sobolev classes with sufficiently differentiable (or even smooth) weights. To this end, suitable classes of differentiable measures will be introduced. The associated Sobolev classes are defined by means of completions in Sobolev norms or via integration by parts formulae. The Gaussian case will be also considered. Basic results will be presented and challenging open problems will be mentioned.