Topics In Modern Regularity Theory

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Topics in Modern Regularity Theory

Giuseppe Mingione
Topics in Modern Regularity Theory Book PDF

Author : Giuseppe Mingione
Publisher : Springer Science & Business Media
Page : 211 pages
File Size : 48,9 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9788876424274

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Topics in Modern Regularity Theory by Giuseppe Mingione Pdf

This book contains lecture notes of a series of courses on the regularity theory of partial differential equations and variational problems, held in Pisa and Parma in the years 2009 and 2010. The contributors, Nicola Fusco, Tristan Rivière and Reiner Schätzle, provide three updated and extensive introductions to various aspects of modern Regularity Theory concerning: mathematical modelling of thin films and related free discontinuity problems, analysis of conformally invariant variational problems via conservation laws, and the analysis of the Willmore functional. Each contribution begins with a very comprehensive introduction, and is aimed to take the reader from the introductory aspects of the subject to the most recent developments of the theory.

Contemporary Research in Elliptic PDEs and Related Topics

Serena Dipierro
Contemporary Research in Elliptic PDEs and Related Topics Book PDF

Author : Serena Dipierro
Publisher : Springer
Page : 502 pages
File Size : 44,7 Mb
Release : 2019-07-12
Category : Mathematics
ISBN : 9783030189211

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Contemporary Research in Elliptic PDEs and Related Topics by Serena Dipierro Pdf

This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.

Free Discontinuity Problems

Nicola Fusco,Aldo Pratelli
Free Discontinuity Problems Book PDF

Author : Nicola Fusco,Aldo Pratelli
Publisher : Springer
Page : 237 pages
File Size : 41,5 Mb
Release : 2017-02-02
Category : Mathematics
ISBN : 9788876425936

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Free Discontinuity Problems by Nicola Fusco,Aldo Pratelli Pdf

This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.

Topics in Modern Differential Geometry

Stefan Haesen,Leopold Verstraelen
Topics in Modern Differential Geometry Book PDF

Author : Stefan Haesen,Leopold Verstraelen
Publisher : Springer
Page : 284 pages
File Size : 53,8 Mb
Release : 2016-12-21
Category : Mathematics
ISBN : 9789462392403

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Topics in Modern Differential Geometry by Stefan Haesen,Leopold Verstraelen Pdf

A variety of introductory articles is provided on a wide range of topics, including variational problems on curves and surfaces with anisotropic curvature. Experts in the fields of Riemannian, Lorentzian and contact geometry present state-of-the-art reviews of their topics. The contributions are written on a graduate level and contain extended bibliographies. The ten chapters are the result of various doctoral courses which were held in 2009 and 2010 at universities in Leuven, Serbia, Romania and Spain.

Geometric Measure Theory and Real Analysis

Luigi Ambrosio
Geometric Measure Theory and Real Analysis Book PDF

Author : Luigi Ambrosio
Publisher : Springer
Page : 228 pages
File Size : 51,6 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9788876425233

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Geometric Measure Theory and Real Analysis by Luigi Ambrosio Pdf

In 2013, a school on Geometric Measure Theory and Real Analysis, organized by G. Alberti, C. De Lellis and myself, took place at the Centro De Giorgi in Pisa, with lectures by V. Bogachev, R. Monti, E. Spadaro and D. Vittone. The book collects the notes of the courses. The courses provide a deep and up to date insight on challenging mathematical problems and their recent developments: infinite-dimensional analysis, minimal surfaces and isoperimetric problems in the Heisenberg group, regularity of sub-Riemannian geodesics and the regularity theory of minimal currents in any dimension and codimension.

A Panorama of Modern Operator Theory and Related Topics

Harry Dym,Marinus A. Kaashoek,Peter Lancaster,Heinz Langer,Leonid Lerer
A Panorama of Modern Operator Theory and Related Topics Book PDF

Author : Harry Dym,Marinus A. Kaashoek,Peter Lancaster,Heinz Langer,Leonid Lerer
Publisher : Springer Science & Business Media
Page : 635 pages
File Size : 48,8 Mb
Release : 2012-02-01
Category : Mathematics
ISBN : 9783034802215

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A Panorama of Modern Operator Theory and Related Topics by Harry Dym,Marinus A. Kaashoek,Peter Lancaster,Heinz Langer,Leonid Lerer Pdf

This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory.

Elliptic Regularity Theory

Lisa Beck
Elliptic Regularity Theory Book PDF

Author : Lisa Beck
Publisher : Springer
Page : 201 pages
File Size : 54,5 Mb
Release : 2016-04-08
Category : Mathematics
ISBN : 9783319274850

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Elliptic Regularity Theory by Lisa Beck Pdf

These lecture notes provide a self-contained introduction to regularity theory for elliptic equations and systems in divergence form. After a short review of some classical results on everywhere regularity for scalar-valued weak solutions, the presentation focuses on vector-valued weak solutions to a system of several coupled equations. In the vectorial case, weak solutions may have discontinuities and so are expected, in general, to be regular only outside of a set of measure zero. Several methods are presented concerning the proof of such partial regularity results, and optimal regularity is discussed. Finally, a short overview is given on the current state of the art concerning the size of the singular set on which discontinuities may occur. The notes are intended for graduate and postgraduate students with a solid background in functional analysis and some familiarity with partial differential equations; they will also be of interest to researchers working on related topics.

Resurgence, Physics and Numbers

Frédéric Fauvet,Dominique Manchon,Stefano Marmi,David Sauzin
Resurgence Physics and Numbers Book PDF

Author : Frédéric Fauvet,Dominique Manchon,Stefano Marmi,David Sauzin
Publisher : Springer
Page : 384 pages
File Size : 44,7 Mb
Release : 2017-11-17
Category : Science
ISBN : 9788876426131

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Resurgence, Physics and Numbers by Frédéric Fauvet,Dominique Manchon,Stefano Marmi,David Sauzin Pdf

This book is issued from a conference around resurgent functions in Physics and multiple zetavalues, which was held at the Centro di Ricerca Matematica Ennio de Giorgi in Pisa, on May 18-22, 2015. This meeting originally stemmed from the impressive upsurge of interest for Jean Ecalle's alien calculus in Physics, in the last years – a trend that has considerably developed since then. The volume contains both original research papers and surveys, by leading experts in the field, reflecting the themes that were tackled at this event: Stokes phenomenon and resurgence, in various mathematical and physical contexts but also related constructions in algebraic combinatorics and results concerning numbers, specifically multiple zetavalues.

Geometry, Structure and Randomness in Combinatorics

Jiří Matousek,Jaroslav Nešetřil,Marco Pellegrini
Geometry Structure and Randomness in Combinatorics Book PDF

Author : Jiří Matousek,Jaroslav Nešetřil,Marco Pellegrini
Publisher : Springer
Page : 160 pages
File Size : 48,5 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9788876425257

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Geometry, Structure and Randomness in Combinatorics by Jiří Matousek,Jaroslav Nešetřil,Marco Pellegrini Pdf

​This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.

Configuration Spaces

Anders Björner,Fred Cohen,Corrado De Concini,Claudo Procesi,Mario Salvetti
Configuration Spaces Book PDF

Author : Anders Björner,Fred Cohen,Corrado De Concini,Claudo Procesi,Mario Salvetti
Publisher : Springer
Page : 547 pages
File Size : 53,7 Mb
Release : 2013-12-18
Category : Mathematics
ISBN : 9788876424311

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Configuration Spaces by Anders Björner,Fred Cohen,Corrado De Concini,Claudo Procesi,Mario Salvetti Pdf

These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May-June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians.

Geometric Partial Differential Equations

Antonin Chambolle,Matteo Novaga,Enrico Valdinoci
Geometric Partial Differential Equations Book PDF

Author : Antonin Chambolle,Matteo Novaga,Enrico Valdinoci
Publisher : Springer Science & Business Media
Page : 400 pages
File Size : 48,6 Mb
Release : 2014-01-17
Category : Mathematics
ISBN : 9788876424731

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Geometric Partial Differential Equations by Antonin Chambolle,Matteo Novaga,Enrico Valdinoci Pdf

This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs

Emanuel Indrei,Diego Marcon,Levon Nurbekyan
Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs Book PDF

Author : Emanuel Indrei,Diego Marcon,Levon Nurbekyan
Publisher : American Mathematical Society
Page : 148 pages
File Size : 45,5 Mb
Release : 2023-01-09
Category : Mathematics
ISBN : 9781470466527

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Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs by Emanuel Indrei,Diego Marcon,Levon Nurbekyan Pdf

This volume contains the proceedings of the virtual conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, held from February 28–March 1, 2021, and hosted by Purdue University, West Lafayette, IN. The mathematical content of this volume is at the intersection of viscosity theory, Fourier analysis, mass transport theory, fractional elliptic theory, and geometric analysis. The reader will encounter, among others, the following topics: the principal-agent problem; Maxwell's equations; Liouville-type theorems for fully nonlinear elliptic equations; a doubly monotone flow for constant width bodies; and the edge dislocations problem for crystals that describes the equilibrium configurations by a nonlocal fractional Laplacian equation.

Topics in Contemporary Mathematical Analysis and Applications

Hemen Dutta
Topics in Contemporary Mathematical Analysis and Applications Book PDF

Author : Hemen Dutta
Publisher : CRC Press
Page : 339 pages
File Size : 45,7 Mb
Release : 2020-12-22
Category : Mathematics
ISBN : 9781000204216

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Topics in Contemporary Mathematical Analysis and Applications by Hemen Dutta Pdf

Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable extent with various new problems for further study. Each chapter carefully presents the related problems and issues, methods of solutions, and their possible applications or relevancies in other scientific areas. Aims at enriching the understanding of methods, problems, and applications Offers an understanding of research problems by presenting the necessary developments in reasonable details Discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems This book is written for individual researchers, educators, students, and department libraries.

Lecture Notes On Regularity Theory For The Navier-stokes Equations

Gregory Seregin
Lecture Notes On Regularity Theory For The Navier stokes Equations Book PDF

Author : Gregory Seregin
Publisher : World Scientific
Page : 268 pages
File Size : 42,6 Mb
Release : 2014-09-16
Category : Mathematics
ISBN : 9789814623421

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Lecture Notes On Regularity Theory For The Navier-stokes Equations by Gregory Seregin Pdf

The lecture notes in this book are based on the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009-2011 at the Mathematical Institute of Oxford University. It contains more or less an elementary introduction to the mathematical theory of the Navier-Stokes equations as well as the modern regularity theory for them. The latter is developed by means of the classical PDE's theory in the style that is quite typical for St Petersburg's mathematical school of the Navier-Stokes equations.The global unique solvability (well-posedness) of initial boundary value problems for the Navier-Stokes equations is in fact one of the seven Millennium problems stated by the Clay Mathematical Institute in 2000. It has not been solved yet. However, a deep connection between regularity and well-posedness is known and can be used to attack the above challenging problem. This type of approach is not very well presented in the modern books on the mathematical theory of the Navier-Stokes equations. Together with introduction chapters, the lecture notes will be a self-contained account on the topic from the very basic stuff to the state-of-art in the field.

Powers

George Molnar
Powers Book PDF

Author : George Molnar
Publisher : Clarendon Press
Page : 252 pages
File Size : 45,9 Mb
Release : 2006-11-30
Category : Philosophy
ISBN : 9780191514012

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Powers by George Molnar Pdf

George Molnar came to see that the solution to a number of the problems of contemporary philosophy lay in the development of an alternative to Hume's metaphysics. This alternative would have real causal powers at its centre. Molnar set about developing a thorough account of powers that might persuade those who remained, perhaps unknowingly, in the grip of Humean assumptions. He succeeded in producing something both highly focused and at the same time wide-ranging. He showed both that the notion of a power was central and that it could serve to dispel a number of long-standing philosophical problems. Molnar's account of powers is as realist as any that has so far appeared. He shows that dispositions are as real as any other properties. Specifically, they do not depend for their existence on their manifestations. Nevertheless, they are directed towards such manifestations. Molnar thus appropriates the notion of intentionality, from Brentano, and argues that it is the essential characteristic of powers. He offers a persuasive case for there being some basic and ungrounded powers, thus ruling out the reducibility of the dispositional to the non-dispositional. However, he does allow that there are non-power properties as well as power properties. In this respect, his final position is dualistic. This is contemporary metaphysics of the highest quality. It is a work that was almost complete when its author died. It has been edited for publication by another specialist in the subject, Stephen Mumford, who has also provided an introduction that will allow non-specialists to become acquainted with the issues. David Armstrong, one of the greatest living metaphysicians and personal friend of George Molnar, has provided a Foreword.