Potential Theory Surveys And Problems

Author : Josef Kral,Jaroslav Lukes,Ivan Netuka,Jiri Vesely
Publisher : Springer
Page : 276 pages
File Size : 50,9 Mb
Release : 2007-02-08
Category : Mathematics
ISBN : 9783540459521

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Potential Theory, Surveys and Problems by Josef Kral,Jaroslav Lukes,Ivan Netuka,Jiri Vesely Pdf

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 : Dr Josef Kral,Jaroslav Lukes,Ivan Netuka
Publisher : Springer
Page : 290 pages
File Size : 40,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662184931

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Potential Theory, Surveys and Problems by Dr Josef Kral,Jaroslav Lukes,Ivan Netuka Pdf

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 : Josef Kral,Jaroslav Lukes,Ivan Netuka,Jiri Vesely
Publisher : Walter de Gruyter
Page : 513 pages
File Size : 40,6 Mb
Release : 2011-10-13
Category : Mathematics
ISBN : 9783110818574

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Potential Theory - ICPT 94 by Josef Kral,Jaroslav Lukes,Ivan Netuka,Jiri Vesely Pdf

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 : David R. Adams,Lars I. Hedberg
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662032824

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Function Spaces and Potential Theory by David R. Adams,Lars I. Hedberg Pdf

"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society

Author : Paolo M. Soardi
Publisher : Springer
Page : 199 pages
File Size : 40,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540487982

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Potential Theory on Infinite Networks by Paolo M. Soardi Pdf

The aim of the book is to give a unified approach to new developments in discrete potential theory and infinite network theory. The author confines himself to the finite energy case, but this does not result in loss of complexity. On the contrary, the functional analytic machinery may be used in analogy with potential theory on Riemann manifolds. The book is intended for researchers with interdisciplinary interests in one of the following fields: Markov chains, combinatorial graph theory, network theory, Dirichlet spaces, potential theory, abstract harmonic analysis, theory of boundaries.

Author : Masanori Kishi
Publisher : Walter de Gruyter
Page : 417 pages
File Size : 49,7 Mb
Release : 2011-05-02
Category : Mathematics
ISBN : 9783110859065

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Potential Theory by Masanori Kishi Pdf

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 : S.S. Vinogradov,P. D. Smith,E.D. Vinogradova
Publisher : CRC Press
Page : 393 pages
File Size : 45,6 Mb
Release : 2001-05-30
Category : Mathematics
ISBN : 9780849387074

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Canonical Problems in Scattering and Potential Theory Part 1 by S.S. Vinogradov,P. D. Smith,E.D. Vinogradova Pdf

Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough in analytical techniques for accurately determining diffraction from classes of canonical scatterers

Author : Luca Capogna,Loredana Lanzani
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 54,8 Mb
Release : 2001
Category : Mathematics
ISBN : 9780821827451

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Harmonic Analysis and Boundary Value Problems by Luca Capogna,Loredana Lanzani Pdf

This volume presents research and expository articles by the participants of the 25th Arkansas Spring Lecture Series on ``Recent Progress in the Study of Harmonic Measure from a Geometric and Analytic Point of View'' held at the University of Arkansas (Fayetteville). Papers in this volume provide clear and concise presentations of many problems that are at the forefront of harmonic analysis and partial differential equations. The following topics are featured: the solution of the Kato conjecture, the ``two bricks'' problem, new results on Cauchy integrals on non-smooth curves, the Neumann problem for sub-Laplacians, and a new general approach to both divergence and nondivergence second order parabolic equations based on growth theorems. The articles in this volume offer both students and researchers a comprehensive volume of current results in the field.

Author : Dorina Mitrea,Marius Mitrea,Michael Taylor
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 52,9 Mb
Release : 2001
Category : Boundary value problems
ISBN : 9780821826591

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Layer Potentials, the Hodge Laplacian, and Global Boundary Problems in Nonsmooth Riemannian Manifolds by Dorina Mitrea,Marius Mitrea,Michael Taylor Pdf

The general aim of the present monograph is to study boundary-value problems for second-order elliptic operators in Lipschitz sub domains of Riemannian manifolds. In the first part (ss1-4), we develop a theory for Cauchy type operators on Lipschitz submanifolds of co dimension one (focused on boundedness properties and jump relations) and solve the $Lp$-Dirichlet problem, with $p$ close to $2$, for general second-order strongly elliptic systems. The solution is represented in the form of layer potentials and optimal non tangential maximal function estimates are established.This analysis is carried out under smoothness assumptions (for the coefficients of the operator, metric tensor and the underlying domain) which are in the nature of best possible. In the second part of the monograph, ss5-13, we further specialize this discussion to the case of Hodge Laplacian $\Delta: =-d\delta-\delta d$. This time, the goal is to identify all (pairs of) natural boundary conditions of Neumann type. Owing to the structural richness of the higher degree case we are considering, the theory developed here encompasses in a unitary fashion many basic PDE's of mathematical physics. Its scope extends to also cover Maxwell's equations, dealt with separately in s14. The main tools are those of PDE's and harmonic analysis, occasionally supplemented with some basic facts from algebraic topology and differential geometry.

Author : Mikhail S. Agranovich
Publisher : Springer
Page : 331 pages
File Size : 42,5 Mb
Release : 2015-05-06
Category : Mathematics
ISBN : 9783319146485

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Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains by Mikhail S. Agranovich Pdf

This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 982 pages
File Size : 54,9 Mb
Release : 1994-02-28
Category : Mathematics
ISBN : 1556080107

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Encyclopaedia of Mathematics (set) by Michiel Hazewinkel Pdf

The Encyclopaedia of Mathematics is the most up-to-date, authoritative and comprehensive English-language work of reference in mathematics which exists today. With over 7,000 articles from `A-integral' to `Zygmund Class of Functions', supplemented with a wealth of complementary information, and an index volume providing thorough cross-referencing of entries of related interest, the Encyclopaedia of Mathematics offers an immediate source of reference to mathematical definitions, concepts, explanations, surveys, examples, terminology and methods. The depth and breadth of content and the straightforward, careful presentation of the information, with the emphasis on accessibility, makes the Encyclopaedia of Mathematics an immensely useful tool for all mathematicians and other scientists who use, or are confronted by, mathematics in their work. The Enclyclopaedia of Mathematics provides, without doubt, a reference source of mathematical knowledge which is unsurpassed in value and usefulness. It can be highly recommended for use in libraries of universities, research institutes, colleges and even schools.

Author : M. Hazewinkel
Publisher : Springer
Page : 932 pages
File Size : 54,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781489937919

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Encyclopaedia of Mathematics by M. Hazewinkel Pdf

Author : Juha Heinonen,Tero Kipelainen,Olli Martio
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 54,8 Mb
Release : 2018-05-16
Category : Mathematics
ISBN : 9780486824253

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Nonlinear Potential Theory of Degenerate Elliptic Equations by Juha Heinonen,Tero Kipelainen,Olli Martio Pdf

A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 620 pages
File Size : 41,6 Mb
Release : 1988
Category : Mathematics
ISBN : 1556080050

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.

Author : Gershon Kresin,V. G. Maz_i_a_
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 54,8 Mb
Release : 2012-08-15
Category : Mathematics
ISBN : 9780821889817

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Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems by Gershon Kresin,V. G. Maz_i_a_ Pdf

The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.