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| Author | : Juha Heinonen |
| Publisher | : Courier Dover Publications |
| Total Pages | : 417 |
| Release | : 2018-05-16 |
| Genre | : Mathematics |
| ISBN | : 0486830462 |
A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.
| Author | : Josef Kral |
| Publisher | : Walter de Gruyter |
| Total Pages | : 513 |
| Release | : 2011-10-13 |
| Genre | : Mathematics |
| ISBN | : 3110818574 |
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
| Author | : Jan Malý |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 309 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821803352 |
The primary objective of this monograph is to give a comprehensive exposition of results surrounding the work of the authors concerning boundary regularity of weak solutions of second order elliptic quasilinear equations in divergence form. The book also contains a complete development of regularity of solutions of variational inequalities, including the double obstacle problem, where the obstacles are allowed to be discontinuous. The book concludes with a chapter devoted to the existence theory thus providing the reader with a complete treatment of the subject ranging from regularity of weak solutions to the existence of weak solutions.
| Author | : B. Fuglede |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 207 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401124361 |
This volume consists of the proceedings of the NATO Advanced Research Workshop on Approximation by Solutions of Partial Differential Equations, Quadrature Formulae, and Related Topics, which was held at Hanstholm, Denmark. These proceedings include the main invited talks and contributed papers given during the workshop. The aim of these lectures was to present a selection of results of the latest research in the field. In addition to covering topics in approximation by solutions of partial differential equations and quadrature formulae, this volume is also concerned with related areas, such as Gaussian quadratures, the Pompelu problem, rational approximation to the Fresnel integral, boundary correspondence of univalent harmonic mappings, the application of the Hilbert transform in two dimensional aerodynamics, finely open sets in the limit set of a finitely generated Kleinian group, scattering theory, harmonic and maximal measures for rational functions and the solution of the classical Dirichlet problem. In addition, this volume includes some problems in potential theory which were presented in the Problem Session at Hanstholm.
| Author | : Josef Kral |
| Publisher | : Springer |
| Total Pages | : 276 |
| Release | : 2007-02-08 |
| Genre | : Mathematics |
| ISBN | : 3540459529 |
The volume comprises eleven survey papers based on survey lectures delivered at the Conference in Prague in July 1987, which covered various facets of potential theory, including its applications in other areas. The survey papers deal with both classical and abstract potential theory and its relations to partial differential equations, stochastic processes and other branches such as numerical analysis and topology. A collection of problems from potential theory, compiled on the occasion of the conference, is included, with additional commentaries, in the second part of this volume.
| Author | : Marta Lewicka |
| Publisher | : Springer Nature |
| Total Pages | : 258 |
| Release | : 2020-06-19 |
| Genre | : Mathematics |
| ISBN | : 3030462099 |
This graduate textbook provides a detailed introduction to the probabilistic interpretation of nonlinear potential theory, relying on the recently introduced notion of tug-of-war games with noise. The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases. The presentation is self-contained with many exercises, making the book suitable as a textbook for a graduate course, as well as for self-study. Extensive background and auxiliary material allow the tailoring of courses to individual student levels.
| Author | : Marco Cirant |
| Publisher | : Princeton University Press |
| Total Pages | : 224 |
| Release | : 2023-10-03 |
| Genre | : Mathematics |
| ISBN | : 069124362X |
An examination of the symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories In recent years, there has evolved a symbiotic and productive relationship between fully nonlinear partial differential equations and generalized potential theories. This book examines important aspects of this story. One main purpose is to prove comparison principles for nonlinear potential theories in Euclidian spaces straightforwardly from duality and monotonicity under the weakest possible notion of ellipticity. The book also shows how to deduce comparison principles for nonlinear differential operators, by marrying these two points of view, under the correspondence principle. The authors explain that comparison principles are fundamental in both contexts, since they imply uniqueness for the Dirichlet problem. When combined with appropriate boundary geometries, yielding suitable barrier functions, they also give existence by Perron’s method. There are many opportunities for cross-fertilization and synergy. In potential theory, one is given a constraint set of 2-jets that determines its subharmonic functions. The constraint set also determines a family of compatible differential operators. Because there are many such operators, potential theory strengthens and simplifies the operator theory. Conversely, the set of operators associated with the constraint can influence the potential theory.
| Author | : Josef Kral |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 352 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461309816 |
Within the tradition of meetings devoted to potential theory, a conference on potential theory took place in Prague on 19-24, July 1987. The Conference was organized by the Faculty of Mathematics and Physics, Charles University, with the collaboration of the Institute of Mathematics, Czechoslovak Academy of Sciences, the Department of Mathematics, Czech University of Technology, the Union of Czechoslovak Mathematicians and Physicists, the Czechoslovak Scientific and Technical Society, and supported by IMU. During the Conference, 69 scientific communications from different branches of potential theory were presented; the majority of them are in cluded in the present volume. (Papers based on survey lectures delivered at the Conference, its program as well as a collection of problems from potential theory will appear in a special volume of the Lecture Notes Series published by Springer-Verlag). Topics of these communications truly reflect the vast scope of contemporary potential theory. Some contributions deal with applications in physics and engineering, other concern potential theoretic aspects of function theory and complex analysis. Numerous papers are devoted to the theory of partial differential equations. Included are also many articles on axiomatic and abstract potential theory with its relations to probability theory. The present volume may thus be of intrest to mathematicians speciali zing in the above-mentioned fields and also to everybody interested in the present state of potential theory as a whole.
| Author | : Emile M.J. Bertin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 294 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401111189 |
ICPT91, the International Conference on Potential Theory, was held in Amersfoort, the Netherlands, from August 18--24, 1991. The volume consists of two parts, the first of which contains papers which also appear in the special issue of POTENTIAL ANALYSIS. The second part includes a collection of contributions edited and partly produced in Utrecht. Professor Monna wrote a preface reminiscing about his experiences with potential theory, mathematics and mathematicians during the last sixty years. The final pages contain a list of participants and a compact index.
| Author | : Bruno Bianchini |
| Publisher | : Springer Nature |
| Total Pages | : 291 |
| Release | : 2021-01-18 |
| Genre | : Mathematics |
| ISBN | : 3030627047 |
This book demonstrates the influence of geometry on the qualitative behaviour of solutions of quasilinear PDEs on Riemannian manifolds. Motivated by examples arising, among others, from the theory of submanifolds, the authors study classes of coercive elliptic differential inequalities on domains of a manifold M with very general nonlinearities depending on the variable x, on the solution u and on its gradient. The book highlights the mean curvature operator and its variants, and investigates the validity of strong maximum principles, compact support principles and Liouville type theorems. In particular, it identifies sharp thresholds involving curvatures or volume growth of geodesic balls in M to guarantee the above properties under appropriate Keller-Osserman type conditions, which are investigated in detail throughout the book, and discusses the geometric reasons behind the existence of such thresholds. Further, the book also provides a unified review of recent results in the literature, and creates a bridge with geometry by studying the validity of weak and strong maximum principles at infinity, in the spirit of Omori-Yau’s Hessian and Laplacian principles and subsequent improvements.
