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Non Linear Potential Theory
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Book Synopsis Nonlinear Potential Theory on Metric Spaces by : Anders Björn
Download or read book Nonlinear Potential Theory on Metric Spaces written by Anders Björn and published by European Mathematical Society. This book was released on 2011 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The $p$-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory, and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs, and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories. This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for interested readers and as a reference text for active researchers. The presentation is rather self contained, but it is assumed that readers know measure theory and functional analysis. The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces, and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space. Each chapter contains historical notes with relevant references, and an extensive index is provided at the end of the book.
Book Synopsis Nonlinear Potential Theory of Degenerate Elliptic Equations by : Juha Heinonen
Download or read book Nonlinear Potential Theory of Degenerate Elliptic Equations written by Juha Heinonen and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Potential Theory and Weighted Sobolev Spaces by : Bengt O. Turesson
Download or read book Nonlinear Potential Theory and Weighted Sobolev Spaces written by Bengt O. Turesson and published by Springer. This book was released on 2007-05-06 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. These spaces occur as solutions spaces for degenerate elliptic partial differential equations. The Sobolev space theory covers results concerning approximation, extension, and interpolation, Sobolev and Poincaré inequalities, Maz'ya type embedding theorems, and isoperimetric inequalities. In the chapter devoted to potential theory, several weighted capacities are investigated. Moreover, "Kellogg lemmas" are established for various concepts of thinness. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincaré inequalities, and spectral synthesis theorems.
Book Synopsis Nonlinear Evolution Equations and Potential Theory by : J. Kral
Download or read book Nonlinear Evolution Equations and Potential Theory written by J. Kral and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface.- Gottfried Anger: Direct and inverse problems in potential theory.- Viorel Barbu: Regularity results for sane differential equations associated with maximal monotone operators in Hilbert spaces.- Haim Brezis: Classes d'interpolation associées à un opérateur monotone et applications.- Siegfried Dnümmel: On inverse problems for k-dimensional potentials.- Jozef Ka?ur: Application of Rothe's method to nonlinear parabolic boundary value problems.- Josef Král: Potentials and removability of singularities.- Vladimir Lovicar: Theorem of Fréchet and asymptotically almost periodid solutions of.
Book Synopsis Non-linear Potential Theory by : F. van Gool
Download or read book Non-linear Potential Theory written by F. van Gool and published by . This book was released on 1990 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Potential Theory of Degenerate Elliptic Equations by : Juha Heinonen
Download or read book Nonlinear Potential Theory of Degenerate Elliptic Equations written by Juha Heinonen and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Axiomatic Approach to Non-linear Potential Theory by : Pasi Lehtola
Download or read book An Axiomatic Approach to Non-linear Potential Theory written by Pasi Lehtola and published by . This book was released on 1986 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Potential Theory and Weighted Sobolev Spaces by : Bengt Ove Turesson
Download or read book Nonlinear Potential Theory and Weighted Sobolev Spaces written by Bengt Ove Turesson and published by . This book was released on 1995 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Potential Theory and Quasiregular Mappings on Riemannian Manifolds by : Ilkka Holopainen
Download or read book Nonlinear Potential Theory and Quasiregular Mappings on Riemannian Manifolds written by Ilkka Holopainen and published by . This book was released on 1990 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis F-harmonic Measure in a Non-linear Potential Theory by : Juha Heinonen
Download or read book F-harmonic Measure in a Non-linear Potential Theory written by Juha Heinonen and published by . This book was released on 1986 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Evolution Equations and Potential Theory by : J. Kral
Download or read book Nonlinear Evolution Equations and Potential Theory written by J. Kral and published by . This book was released on 1975-04-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topics in Non-linear Potential Theory by : Franciscus Antonius van Gool
Download or read book Topics in Non-linear Potential Theory written by Franciscus Antonius van Gool and published by . This book was released on 1992 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Null-sets in a Non-linear Potential Theory by : Juha Heinonen
Download or read book Null-sets in a Non-linear Potential Theory written by Juha Heinonen and published by . This book was released on 1986 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Thin Sets in Nonlinear Potential Theory by : Lars Inge Hedberg
Download or read book Thin Sets in Nonlinear Potential Theory written by Lars Inge Hedberg and published by . This book was released on 1982 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Thinness in Non-linear Potential Theory for Non-isotropic Sobolev Spaces by : Tord Sjödin
Download or read book Thinness in Non-linear Potential Theory for Non-isotropic Sobolev Spaces written by Tord Sjödin and published by . This book was released on 1998 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Potential Theory by : Masanori Kishi
Download or read book Potential Theory written by Masanori Kishi and published by Walter de Gruyter. This book was released on 2011-05-02 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Potential Theory written by Josef Kral and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
