Notes on the Infinity Laplace Equation

Notes on the Infinity Laplace Equation
Author: Peter Lindqvist
Publisher: Springer
Total Pages: 73
Release: 2016-05-25
Genre: Mathematics
ISBN: 3319315323

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.

A Course on Tug-of-War Games with Random Noise

A Course on Tug-of-War Games with Random Noise
Author: Marta Lewicka
Publisher: Springer Nature
Total Pages: 258
Release: 2020-06-19
Genre: Mathematics
ISBN: 3030462099

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.

Regularity Estimates for Nonlinear Elliptic and Parabolic Problems

Regularity Estimates for Nonlinear Elliptic and Parabolic Problems
Author: John Lewis
Publisher: Springer Science & Business Media
Total Pages: 259
Release: 2012-03-02
Genre: Mathematics
ISBN: 3642271448

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.

Nonlinear Elliptic Partial Differential Equations

Nonlinear Elliptic Partial Differential Equations
Author: J. P. Gossez
Publisher: American Mathematical Soc.
Total Pages: 278
Release: 2011
Genre: Mathematics
ISBN: 0821849077

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.

Advanced Courses Of Mathematical Analysis V - Proceedings Of The Fifth International School

Advanced Courses Of Mathematical Analysis V - Proceedings Of The Fifth International School
Author: Juan Carlos Navarro Pascual
Publisher: World Scientific
Total Pages: 319
Release: 2016-06-24
Genre: Mathematics
ISBN: 9814699705

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.

Notes on the Stationary p-Laplace Equation

Notes on the Stationary p-Laplace Equation
Author: Peter Lindqvist
Publisher: Springer
Total Pages: 107
Release: 2019-04-26
Genre: Mathematics
ISBN: 3030145018

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

Second Order Parabolic Differential Equations

Second Order Parabolic Differential Equations
Author: Gary M. Lieberman
Publisher: World Scientific
Total Pages: 472
Release: 1996
Genre: Mathematics
ISBN: 9789810228835

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.

Complexity

Complexity
Author: M. Mitchell Waldrop
Publisher: Open Road Media
Total Pages: 492
Release: 2019-10-01
Genre: Science
ISBN: 150405914X

“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