Notes on Tug-of-War Games and the p-Laplace Equation PDF Download

Author: Mikko Parviainen
Publisher: Springer Nature
ISBN: 9819978793
Category :
Languages : en
Pages : 83

View

Book Description

Author: Peter Lindqvist
Publisher: Springer
ISBN: 3319315323
Category : Mathematics
Languages : en
Pages : 68

View

Book Description
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.

Author: Marta Lewicka
Publisher: Springer Nature
ISBN: 3030462099
Category : Mathematics
Languages : en
Pages : 258

View

Book Description
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.

Author: John Lewis
Publisher: Springer Science & Business Media
ISBN: 3642271448
Category : Mathematics
Languages : en
Pages : 259

View

Book Description
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.

Author: J. P. Gossez
Publisher: American Mathematical Soc.
ISBN: 0821849077
Category : Differential equations, Elliptic
Languages : en
Pages : 278

View

Book Description
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.

Author: Juan Carlos Navarro Pascual
Publisher: World Scientific
ISBN: 9814699705
Category : Mathematics
Languages : en
Pages : 320

View

Book Description
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. Contents:Measurability and Semi-Continuity of Multifunctions (B Cascales)Introduction to Interpolation Theory (F Cobos)Optimality of Function Spaces in Sobolev Embeddings (L Pick)Derivations and Projections on Jordan Triples: An introduction to Nonassociative Algebra, Continuous Cohomology, and Quantum Functional Analysis (B Russo)Weighted Inequalities and Extrapolation (J Duoandikoetxea)A Note on the Off-Diagonal Muckenhoupt–Wheeden Conjecture (D Cruz-Uribe, J M Martell and C Pérez)On the Interplay Between Nonlinear Partial Differential Equations and Game Theory (J D Rossi)The Radon–Nikodým Theorem for Vector Measures and Integral Representation of Operators on Banach Function Spaces (E A Sánchez Pérez)The Orlicz–Pettis Theorem for Multiplier Convergent Series (C Swartz) Readership: Graduate students in mathematics and researchers in mathematical analysis.

Author: Pablo Blanc
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110619326
Category : Mathematics
Languages : en
Pages : 273

View

Book Description
The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-ChiefJ rgen Appell, W rzburg, Germany Honorary and Advisory EditorsCatherine Bandle, Basel, SwitzerlandAlain Bensoussan, Richardson, Texas, USAAvner Friedman, Columbus, Ohio, USAUmberto Mosco, Worcester, Massachusetts, USALouis Nirenberg, New York, USAAlfonso Vignoli, Rome, Italy Editorial BoardManuel del Pino, Bath, UK, and Santiago, ChileMikio Kato, Nagano, JapanWojciech Kryszewski, Toruń, PolandVicenţiu D. Rădulescu, Krak w, PolandSimeon Reich, Haifa, Israel Please submit book proposals to J rgen Appell. Titles in planning include Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019)Tomasz W. Dlotko and Yejuan Wang, Critical Parabolic-Type Problems (2019)Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019)Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020)Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

Author: Peter Lindqvist
Publisher:
ISBN: 9789513925864
Category : Differential equations, Elliptic
Languages : fi
Pages : 80

View

Book Description

Author: Peter Lindqvist
Publisher: Springer
ISBN: 3030145018
Category : Mathematics
Languages : en
Pages : 104

View

Book Description
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

Author: Francisco Javier Garcia-Pacheco
Publisher: CRC Press
ISBN: 1000432262
Category : Mathematics
Languages : en
Pages : 396

View

Book Description
Abstract Calculus: A Categorical Approach provides an abstract approach to calculus. It is intended for graduate students pursuing PhDs in pure mathematics but junior and senior researchers in basically any field of mathematics and theoretical physics will also be interested. Any calculus text for undergraduate students majoring in engineering, mathematics or physics deals with the classical concepts of limits, continuity, differentiability, optimization, integrability, summability, and approximation. This book covers the exact same topics, but from a categorical perspective, making the classification of topological modules as the main category involved. Features Suitable for PhD candidates and researchers Requires prerequisites in set theory, general topology, and abstract algebra, but is otherwise self-contained Dr. Francisco Javier García-Pacheco is a full professor and Director of the Departmental Section of Mathematics at the College of Engineering of the University of Cádiz, Spain.