Newtonian Spaces

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Nonlinear Potential Theory On Metric Spaces

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Author : Anders Björn
language : en
Publisher: European Mathematical Society
Release Date : 2011

Nonlinear Potential Theory On Metric Spaces written by Anders Björn and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

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.

Sobolev Spaces In Mathematics I

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Author : Vladimir Maz'ya
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-02

Sobolev Spaces In Mathematics I written by Vladimir Maz'ya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-02 with Mathematics categories.

This volume mark’s the centenary of the birth of the outstanding mathematician of the 20th century, Sergey Sobolev. It includes new results on the latest topics of the theory of Sobolev spaces, partial differential equations, analysis and mathematical physics.

Newtonian Spaces

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Author : Nageswari Shanmugalingam
language : en
Publisher:
Release Date : 1999

Newtonian Spaces written by Nageswari Shanmugalingam and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.

Sobolev Spaces On Metric Measure Spaces

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Author : Juha Heinonen
language : en
Publisher: Cambridge University Press
Release Date : 2015-02-05

Sobolev Spaces On Metric Measure Spaces written by Juha Heinonen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-05 with Mathematics categories.

This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.

Function Spaces Interpolation Theory And Related Topics

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Author : Michael Cwikel
language : en
Publisher: Walter de Gruyter
Release Date : 2008-08-22

Function Spaces Interpolation Theory And Related Topics written by Michael Cwikel and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-22 with Mathematics categories.

This volume contains 16 refereed research articles on function spaces, interpolation theory and related fields. Topics covered: theory of function spaces, Hankel-type and related operators, analysis on bounded symmetric domains, partial differential equations, Green functions, special functions, homogenization theory, Sobolev embeddings, Coxeter groups, spectral theory and wavelets. The book will be of interest to both researchers and graduate students working in interpolation theory, function spaces and operators, partial differential equations and analysis on bounded symmetric domains.

Space Perception And The Philosophy Of Science

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Author : Patrick A. Heelan
language : en
Publisher: Univ of California Press
Release Date : 1983

Space Perception And The Philosophy Of Science written by Patrick A. Heelan and has been published by Univ of California Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Philosophy categories.

Drawing on the phenomenological tradition in the philosophy of science and philosophy of nature, Patrick Heelan concludes that perception is a cognitive, world-building act, and is therefore never absolute or finished.

Minkowski Space

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Author : Joachim Schröter
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-06-12

Minkowski Space written by Joachim Schröter and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-12 with Science categories.

In Minkowski-Space the space-time of special relativity is discussed on the basis of fundamental results of space-time theory. This idea has the consequence that the Minkowski-space can be characterized by 5 axioms, which determine its geometrical and kinematical structure completely. In this sense Minkowski-Space is a prolegomenon for the formulation of other branches of special relativity, like mechanics, electrodynamics, thermodynamics etc. But these applications are not subjects of this book. Contents Basic properties of special relativity Further properties of Lorentz matrices Further properties of Lorentz transformations Decomposition of Lorentz matrices and Lorentz transformations Further structures on Ms Tangent vectors in Ms Orientation Kinematics on Ms Some basic notions of relativistic theories

Potential Theory On Sierpi Ski Carpets

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Author : Dimitrios Ntalampekos
language : en
Publisher: Springer Nature
Release Date : 2020-09-01

Potential Theory On Sierpi Ski Carpets written by Dimitrios Ntalampekos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.

This self-contained book lays the foundations for a systematic understanding of potential theoretic and uniformization problems on fractal Sierpiński carpets, and proposes a theory based on the latest developments in the field of analysis on metric spaces. The first part focuses on the development of an innovative theory of harmonic functions that is suitable for Sierpiński carpets but differs from the classical approach of potential theory in metric spaces. The second part describes how this theory is utilized to prove a uniformization result for Sierpiński carpets. This book is intended for researchers in the fields of potential theory, quasiconformal geometry, geometric group theory, complex dynamics, geometric function theory and PDEs.

Vacuum Space Time Matter And The Models Of Smarandache Geometry Smarandache

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Author : Hu Chang-Wei ( 胡昌伟 )
language : en
Publisher: Infinite Study
Release Date :

Vacuum Space Time Matter And The Models Of Smarandache Geometry Smarandache written by Hu Chang-Wei ( 胡昌伟 ) and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Special Relativity

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Author : Michael Tsamparlis
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-17

Special Relativity written by Michael Tsamparlis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-17 with Science categories.

Writing a new book on the classic subject of Special Relativity, on which numerous important physicists have contributed and many books have already been written, can be like adding another epicycle to the Ptolemaic cosmology. Furthermore, it is our belief that if a book has no new elements, but simply repeats what is written in the existing literature, perhaps with a different style, then this is not enough to justify its publication. However, after having spent a number of years, both in class and research with relativity, I have come to the conclusion that there exists a place for a new book. Since it appears that somewhere along the way, mathem- ics may have obscured and prevailed to the degree that we tend to teach relativity (and I believe, theoretical physics) simply using “heavier” mathematics without the inspiration and the mastery of the classic physicists of the last century. Moreover current trends encourage the application of techniques in producing quick results and not tedious conceptual approaches resulting in long-lasting reasoning. On the other hand, physics cannot be done a ́ la carte stripped from philosophy, or, to put it in a simple but dramatic context A building is not an accumulation of stones! As a result of the above, a major aim in the writing of this book has been the distinction between the mathematics of Minkowski space and the physics of r- ativity.