Classical and Modern Potential Theory and Applications

✍ Scribed by D. R. Adams (auth.), K. GowriSankaran, J. Bliedtner, D. Feyel, M. Goldstein, W. K. Hayman, I. Netuka (eds.)

• Publisher: Springer Netherlands
• Year: 1994
• Tongue: English
• Leaves: 466
• Series: NATO ASI Series 430
• Edition: 1
• Category: Library

✦ Synopsis

This is a collection of research papers based on the talks given at the NATO Advanced Research Workshop held at Château de Bonas in France in July of 1993 and approved for publication by a panel of referees. The contributions are by some of the most prominent and active research workers in the subject from the NATO countries and a limited number of selected invitees from the rest of the mathematical world. The workshop brought together mathematicians doing work in the classical and the modern aspects of the subject for mutual interaction, and the articles in the volume bear evidence to this fact. This is a valuable book for all the mathematicians with research interest in potential theory.
There are 33 research papers on several aspects of the current research in potential theory. Besides the latest research work of some of the most prominent and respected researchers in the subject, it contains a very valuable and thoroughly researched article on the mean value property of harmonic functions by I. Netuka and J. Vesely. The article by T. Murai on ozone depletion and its study through certain differential equations is very topical and undoubtedly of great interest to many. The volume also contains a large number of state-of-the-art research problems posed by the participants at the workshop.

✦ Table of Contents

Front Matter....Pages i-xiv
Nonlinear PDE and the Wiener Test....Pages 1-9
k-Superharmonic Functions and L. Kelvin’s Theorem....Pages 11-17
On the Invariance of the Solutions of the Weinstein Equation under Möbius Transformations....Pages 19-29
Radial Limiting Behaviour of Harmonic and Super-Harmonic Functions....Pages 31-40
Multiparameter Processes Associated with Ornstein-Uhlenbeck Semigroups....Pages 41-55
On the Problem of Hypoellipticity on the Infinite Dimensional Torus....Pages 57-59
L’équation de Monge-Ampère dans un espace de Banach....Pages 61-75
Excessive Functions and Excessive Measures: Hunt’s Theorem on Balayages, Quasi-Continuity....Pages 77-92
The Wiener Test for Poincaré-Dirichlet Forms....Pages 93-104
The Best Approach for Boundary Limits....Pages 105-112
Fine Behaviour of Balayages in Potential Theory....Pages 113-123
Some Results about Sequential Integration on Wiener Space....Pages 125-132
Schwarz Lemma Type Inequalities for Harmonic Functions in the Ball....Pages 133-147
Duality of H-Cones....Pages 149-157
Régularité et intégrabilité des fonctionnelles de Wiener....Pages 159-164
Poincaré Inequalities in L 1 -Norm for the Sphere and a Strong Isoperimetric Inequality in R n ....Pages 165-183
Uniform and Tangential Harmonic Approximation....Pages 185-198
Inversion and Reflecting Brownian Motion....Pages 199-215
Γ-Potentials....Pages 217-232
Fatou-Doob Limits and the Best Filters....Pages 233-236
Gaussian Upper Bounds for the Heat Kernel and for Its Derivatives on a Riemannian Manifold....Pages 237-252
Integrals of analytic functions along 2 curves....Pages 253-265
On the Restricted Mean Value Property for Measurable Functions....Pages 267-271
A Constructive Method for Univalent Logharmonic Mappings....Pages 273-291
Choquet-Type Integral Representation of Polyexcessive Functions....Pages 293-314
Refining the Local Uniform Convergence Topology....Pages 315-316
Daily rheological phenomena....Pages 317-352
Convergence Property and Superharmonic Functions on Balayage Spaces....Pages 353-357
Mean Value Property and Harmonic Functions....Pages 359-398
Farrell and Mergelyan Sets for the Space of Bounded Harmonic Functions....Pages 399-412
Méthodes Analytiques en dimension infinie....Pages 413-417
Construction d’un processus à deux paramètres à partir d’un semigroupe à un paramètre....Pages 419-451
Capacities and Harmonic Measures for Uniformly Elliptic Operators of Nondivergence Form....Pages 453-459
Problems....Pages 461-470

✦ Subjects

Potential Theory; Probability Theory and Stochastic Processes; Approximations and Expansions; Partial Differential Equations; Analysis