Download or read book Notes on Tug of War Games and the p Laplace Equation written by Mikko Parviainen and published by Springer Nature. This book was released on with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Notes on the Infinity Laplace Equation written by Peter Lindqvist and published by Springer. This book was released on 2016-05-25 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity-Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.
Download or read book A Course on Tug of War Games with Random Noise written by Marta Lewicka and published by Springer Nature. This book was released on 2020-06-19 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Regularity Estimates for Nonlinear Elliptic and Parabolic Problems written by John Lewis and published by Springer Science & Business Media. This book was released on 2012-03-02 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The issue of regularity has played a central role in the theory of Partial Differential Equations almost since its inception, and despite the tremendous advances made it still remains a very fruitful research field. In particular considerable strides have been made in regularity estimates for degenerate and singular elliptic and parabolic equations over the last several years, and in many unexpected and challenging directions. Because of all these recent results, it seemed high time to create an overview that would highlight emerging trends and issues in this fascinating research topic in a proper and effective way. The course aimed to show the deep connections between these topics and to open new research directions through the contributions of leading experts in all of these fields.
Download or read book Nonlinear Elliptic Partial Differential Equations written by J. P. Gossez and published by American Mathematical Soc.. This book was released on 2011 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium. The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the $p$-Laplacian operator, the antimaximum principle, the Fucik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.
Download or read book Advanced Courses Of Mathematical Analysis V Proceedings Of The Fifth International School written by Juan Carlos Navarro Pascual and published by World Scientific. This book was released on 2016-06-24 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains recent papers by several specialists in different fields of mathematical analysis. It offers a reasonably wide perspective of the current state of research, and new trends, in areas related to measure theory, harmonic analysis, non-associative structures in functional analysis and summability in locally convex spaces.Those interested in researching any areas of mathematical analysis will find here numerous suggestions on possible topics with an important impact today. Often, the contributions are presented in an expository nature and this makes the discussed topics accessible to a more general audience.
Download or read book Notes on the Stationary p Laplace Equation written by Peter Lindqvist and published by Springer. This book was released on 2019-04-26 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book in the BCAM SpringerBriefs series is a treatise on the p-Laplace equation. It is based on lectures by the author that were originally delivered at the Summer School in Jyväskylä, Finland, in August 2005 and have since been updated and extended to cover various new topics, including viscosity solutions and asymptotic mean values. The p-Laplace equation is a far-reaching generalization of the ordinary Laplace equation, but it is non-linear and degenerate (p>2) or singular (p2). Thus it requires advanced methods. Many fascinating properties of the Laplace equation are, in some modified version, extended to the p-Laplace equation. Nowadays the theory is almost complete, although some challenging problems remain open./pbrp
Download or read book Notes on the P Laplace Equation written by Peter Lindqvist and published by . This book was released on 2006 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Second Order Parabolic Differential Equations written by Gary M. Lieberman and published by World Scientific. This book was released on 1996 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction. Maximum principles. Introduction to the theory of weak solutions. Hölder estimates. Existence, uniqueness, and regularity of solutions. Further theory of weak solutions. Strong solutions. Fixed point theorems and their applications. Comparison and maximum principles. Boundary gradient estimates. Global and local gradient bounds. Hölder gradient estimates and existence theorems. The oblique derivative problem for quasilinear parabolic equations. Fully nonlinear equations. Introduction. Monge-Ampère and Hessian equations.
Download or read book Complexity written by M. Mitchell Waldrop and published by Open Road Media. This book was released on 2019-10-01 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: “If you liked Chaos, you’ll love Complexity. Waldrop creates the most exciting intellectual adventure story of the year” (The Washington Post). In a rarified world of scientific research, a revolution has been brewing. Its activists are not anarchists, but rather Nobel Laureates in physics and economics and pony-tailed graduates, mathematicians, and computer scientists from all over the world. They have formed an iconoclastic think-tank and their radical idea is to create a new science: complexity. They want to know how a primordial soup of simple molecules managed to turn itself into the first living cell—and what the origin of life some four billion years ago can tell us about the process of technological innovation today. This book is their story—the story of how they have tried to forge what they like to call the science of the twenty-first century. “Lucidly shows physicists, biologists, computer scientists and economists swapping metaphors and reveling in the sense that epochal discoveries are just around the corner . . . [Waldrop] has a special talent for relaying the exhilaration of moments of intellectual insight.” —The New York Times Book Review “Where I enjoyed the book was when it dove into the actual question of complexity, talking about complex systems in economics, biology, genetics, computer modeling, and so on. Snippets of rare beauty here and there almost took your breath away.” —Medium “[Waldrop] provides a good grounding of what may indeed be the first flowering of a new science.” —Publishers Weekly
Download or read book An Introduction To Viscosity Solutions for Fully Nonlinear PDE with Applications to Calculus of Variations in L written by Nikos Katzourakis and published by Springer. This book was released on 2014-11-26 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a quick and elementary, yet rigorous, presentation of the rudiments of the so-called theory of Viscosity Solutions which applies to fully nonlinear 1st and 2nd order Partial Differential Equations (PDE). For such equations, particularly for 2nd order ones, solutions generally are non-smooth and standard approaches in order to define a "weak solution" do not apply: classical, strong almost everywhere, weak, measure-valued and distributional solutions either do not exist or may not even be defined. The main reason for the latter failure is that, the standard idea of using "integration-by-parts" in order to pass derivatives to smooth test functions by duality, is not available for non-divergence structure PDE.
Download or read book Game Theory and Partial Differential Equations written by Pablo Blanc and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extending the well-known connection between classical linear potential theory and probability theory (through the interplay between harmonic functions and martingales) to the nonlinear case of tug-of-war games and their related partial differential equations, this unique book collects several results in this direction and puts them in an elementary perspective in a lucid and self-contained fashion.
Download or read book Nonlocal Diffusion Problems written by Fuensanta Andreu-Vaillo and published by American Mathematical Soc.. This book was released on 2010 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlocal diffusion problems arise in a wide variety of applications, including biology, image processing, particle systems, coagulation models, and mathematical finance. These types of problems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary conditions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the $p$-Laplacian evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson-Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems.
Download or read book Five Equations That Changed the World written by Dr. Michael Guillen and published by Hachette Books. This book was released on 2012-06-05 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Publishers Weekly best book of 1995! Dr. Michael Guillen, known to millions as the science editor of ABC's Good Morning America, tells the fascinating stories behind five mathematical equations. As a regular contributor to daytime's most popular morning news show and an instructor at Harvard University, Dr. Michael Guillen has earned the respect of millions as a clear and entertaining guide to the exhilarating world of science and mathematics. Now Dr. Guillen unravels the equations that have led to the inventions and events that characterize the modern world, one of which -- Albert Einstein's famous energy equation, E=mc2 -- enabled the creation of the nuclear bomb. Also revealed are the mathematical foundations for the moon landing, airplane travel, the electric generator -- and even life itself. Praised by Publishers Weekly as "a wholly accessible, beautifully written exploration of the potent mathematical imagination," and named a Best Nonfiction Book of 1995, the stories behind The Five Equations That Changed the World, as told by Dr. Guillen, are not only chronicles of science, but also gripping dramas of jealousy, fame, war, and discovery.
Download or read book The Essence Of Chaos written by Flavio Lorenzelli and published by CRC Press. This book was released on 2003-09-02 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of chaotic systems has become a major scientific pursuit in recent years, shedding light on the apparently random behaviour observed in fields as diverse as climatology and mechanics. InThe Essence of Chaos Edward Lorenz, one of the founding fathers of Chaos and the originator of its seminal concept of the Butterfly Effect, presents his own landscape of our current understanding of the field. Lorenz presents everyday examples of chaotic behaviour, such as the toss of a coin, the pinball's path, the fall of a leaf, and explains in elementary mathematical strms how their essentially chaotic nature can be understood. His principal example involved the construction of a model of a board sliding down a ski slope. Through this model Lorenz illustrates chaotic phenomena and the related concepts of bifurcation and strange attractors. He also provides the context in which chaos can be related to the similarly emergent fields of nonlinearity, complexity and fractals. As an early pioneer of chaos, Lorenz also provides his own story of the human endeavour in developing this new field. He describes his initial encounters with chaos through his study of climate and introduces many of the personalities who contributed early breakthroughs. His seminal paper, "Does the Flap of a Butterfly's Wing in Brazil Set Off a Tornado in Texas?" is published for the first time.
Download or read book NIELS HENRIK ABEL and his Times written by Arild Stubhaug and published by Springer Science & Business Media. This book was released on 2000-04-26 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everyone with an interest in the history of mathematics and science will enjoy reading this book on one of the most famous mathematicians of the 19th century. The author, who is both a historian and a mathematician, has written the definitive biography of Niels Henrik Abel.
Download or read book Good and Real written by Gary L. Drescher and published by MIT Press. This book was released on 2006 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examining a series of provocative paradoxes about consciousness, choice, ethics, and other topics, Good and Real tries to reconcile a purely mechanical view of the universe with key aspects of our subjective impressions of our own existence. In Good and Real, Gary Drescher examines a series of provocative paradoxes about consciousness, choice, ethics, quantum mechanics, and other topics, in an effort to reconcile a purely mechanical view of the universe with key aspects of our subjective impressions of our own existence. Many scientists suspect that the universe can ultimately be described by a simple (perhaps even deterministic) formalism; all that is real unfolds mechanically according to that formalism. But how, then, is it possible for us to be conscious, or to make genuine choices? And how can there be an ethical dimension to such choices? Drescher sketches computational models of consciousness, choice, and subjunctive reasoning--what would happen if this or that were to occur? --to show how such phenomena are compatible with a mechanical, even deterministic universe. Analyses of Newcomb's Problem (a paradox about choice) and the Prisoner's Dilemma (a paradox about self-interest vs. altruism, arguably reducible to Newcomb's Problem) help bring the problems and proposed solutions into focus. Regarding quantum mechanics, Drescher builds on Everett's relative-state formulation--but presenting a simplified formalism, accessible to laypersons--to argue that, contrary to some popular impressions, quantum mechanics is compatible with an objective, deterministic physical reality, and that there is no special connection between quantum phenomena and consciousness. In each of several disparate but intertwined topics ranging from physics to ethics, Drescher argues that a missing technical linchpin can make the quest for objectivity seem impossible, until the elusive technical fix is at hand.
