Potential Theory and Degenerate Partial Differential Operators

ISBN-13: 9789401040426 / Angielski / Miękka / 2012 / 185 str.

Marco Biroli

Opis

Recent years have witnessed an increasingly close relationship growing between potential theory, probability and degenerate partial differential operators. The theory of Dirichlet (Markovian) forms on an abstract finite or infinite-dimensional space is common to all three disciplines. This is a fascinating and important subject, central to many of the contributions to the conference on 'Potential Theory and Degenerate Partial Differential Operators', held in Parma, Italy, February 1994.

Spis treści

Foreword. Sobolev inequalities on homogeneous spaces; M. Biroli, U. Mosco. Regularity for solutions of quasilinear elliptic equations under minimal assumption; F. Chiarenza. Dimensions at infinity for Riemannian manifolds; T. Coulhon. On infinite dimensional sheets; D. Feyel, A. de la Pradelle. Weighted Poincaré inequalities for Hömander vector fields and local regularity for a class of degenerate elliptic equations; B. Franchi, et al. Reflecting diffusions on Lipschitz domains with cups - analytic construction and Skorohod representation; M. Fukushima, M. Tomisaki. Fermabilité des formes de Dirichlet et inégalité de type Poincaré; G. Mokobodzki. Comparison Hölderienne des distances sous-elliptiques et calcul S(m,g); S. Mustapha, N. Varopoulos. Parabolic Harnack inequality for divergence form second order differential operators; L. Saloff-Coste. Recenti risultata sulle teoria degli operatori vicini; S. Campanato. Existence of bounded solutions for some degenerated quasilinear elliptic equations; P. Drábek, F. Nicolosi.