Potential Theory and Degenerate Partial Differential Operators

by Marco Biroli (Editor)

Overview

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.

Product Details

ISBN-13:	9780792335962
Publisher:	Springer Netherlands
Publication date:	10/31/1995
Edition description:	Reprinted, with additional material, from POTENTIAL ANALYSIS 4:4, 1995
Pages:	185
Product dimensions:	6.69(w) x 9.61(h) x 0.36(d)

Table of Contents

Sobolev Inequalities on Homogeneous Spaces.- Regularity for Solutions of Quasilinear Elliptic Equations under Minimal Assumptions.- Dimensions at Infinity for Riemannian Manifolds.- On Infinite Dimensional Sheets.- Weighted Poincaré Inequalities for Hörmander Vector Fields and Local Regularity for a Class of Degenerate Elliptic Equations.- Reflecting Diffusions on Lipschitz Domains with Cusps — Analytic Construction and Skorohod Representation.- Fermabilité des formes de Dirichlet et inégalité de type Poincaré.- Comparaison Hölderienne des distances sous-elliptiques et calcul S (m,g).- Parabolic Harnack Inequality for Divergence Form Second Order Differential Operators.- Recenti risultati sulla teoria degli operatori vicini.- Existence of Bounded Solutions for Some Degenerated Quasilinear Elliptic Equations.

Editorial Reviews

Eleven lectures presented at the Potential Theory and Degenerate Partial Differential Operators conference, Parma, Italy, February 1994, and partially published in Potential Analysis, v.4, no.4, 1995. The discussions illustrate the theory of Dirichlet (Markovian) forms on an abstract finite or infinite-dimensional space as a common denominator to the disciplines of potential theory, probability, and degenerate partial differential operators. Each lecture demonstrates theory with extensive calculations. Lacks an index. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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