Regularity Techniques For Elliptic Pdes And The Fractional Laplacian
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Regularity Techniques For Elliptic Pdes And The Fractional Laplacian
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Author : Pablo Raúl Stinga
language : en
Publisher: CRC Press
Release Date : 2024-06-21
Regularity Techniques For Elliptic Pdes And The Fractional Laplacian written by Pablo Raúl Stinga and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-21 with Mathematics categories.
Regularity Techniques for Elliptic PDEs and the Fractional Laplacian presents important analytic and geometric techniques to prove regularity estimates for solutions to second order elliptic equations, both in divergence and nondivergence form, and to nonlocal equations driven by the fractional Laplacian. The emphasis is placed on ideas and the development of intuition, while at the same time being completely rigorous. The reader should keep in mind that this text is about how analysis can be applied to regularity estimates. Many methods are nonlinear in nature, but the focus is on linear equations without lower order terms, thus avoiding bulky computations. The philosophy underpinning the book is that ideas must be flushed out in the cleanest and simplest ways, showing all the details and always maintaining rigor. Features Self-contained treatment of the topic Bridges the gap between upper undergraduate textbooks and advanced monographs to offer a useful, accessible reference for students and researchers. Replete with useful references.
Regularity Techniques For Elliptic Pdes And The Fractional Laplacian
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Author : Pablo Raúl Stinga
language : en
Publisher: CRC Press
Release Date : 2024-07-02
Regularity Techniques For Elliptic Pdes And The Fractional Laplacian written by Pablo Raúl Stinga and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-02 with Mathematics categories.
Regularity Techniques for Elliptic PDEs and the Fractional Laplacian presents important analytic and geometric techniques to prove regularity estimates for solutions to second order elliptic equations, both in divergence and nondivergence form, and to nonlocal equations driven by the fractional Laplacian. The emphasis is placed on ideas and the development of intuition, while at the same time being completely rigorous. The reader should keep in mind that this text is about how analysis can be applied to regularity estimates. Many methods are nonlinear in nature, but the focus is on linear equations without lower order terms, thus avoiding bulky computations. The philosophy underpinning the book is that ideas must be flushed out in the cleanest and simplest ways, showing all the details and always maintaining rigor. Features Self-contained treatment of the topic Bridges the gap between upper undergraduate textbooks and advanced monographs to offer a useful, accessible reference for students and researchers. Replete with useful references.
The Fractional Laplacian
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Author : Wenxiong Chen
language : en
Publisher: World Scientific
Release Date : 2020-06-09
The Fractional Laplacian written by Wenxiong Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-09 with Mathematics categories.
This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared recently in research literature, which researchers would find helpful. It focuses on introducing direct methods on the nonlocal problems without going through extensions, such as the direct methods of moving planes, direct method of moving spheres, direct blowing up and rescaling arguments, and so on. Different from most other books, it emphasizes on illuminating the ideas behind the formal concepts and proofs, so that readers can quickly grasp the essence.
Variational Methods For Nonlocal Fractional Problems
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Author : Giovanni Molica Bisci
language : en
Publisher: Cambridge University Press
Release Date : 2016-03-11
Variational Methods For Nonlocal Fractional Problems written by Giovanni Molica Bisci 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 2016-03-11 with Mathematics categories.
A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.
Contemporary Research In Elliptic Pdes And Related Topics
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Author : Serena Dipierro
language : en
Publisher: Springer
Release Date : 2019-07-12
Contemporary Research In Elliptic Pdes And Related Topics written by Serena Dipierro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-12 with Mathematics categories.
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.
75 Years Of Mathematics Of Computation
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Author : Susanne C. Brenner
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-29
75 Years Of Mathematics Of Computation written by Susanne C. Brenner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-29 with Education categories.
The year 2018 marked the 75th anniversary of the founding of Mathematics of Computation, one of the four primary research journals published by the American Mathematical Society and the oldest research journal devoted to computational mathematics. To celebrate this milestone, the symposium “Celebrating 75 Years of Mathematics of Computation” was held from November 1–3, 2018, at the Institute for Computational and Experimental Research in Mathematics (ICERM), Providence, Rhode Island. The sixteen papers in this volume, written by the symposium speakers and editors of the journal, include both survey articles and new contributions. On the discrete side, there are four papers covering topics in computational number theory and computational algebra. On the continuous side, there are twelve papers covering topics in machine learning, high dimensional approximations, nonlocal and fractional elliptic problems, gradient flows, hyperbolic conservation laws, Maxwell's equations, Stokes's equations, a posteriori error estimation, and iterative methods. Together they provide a snapshot of significant achievements in the past quarter century in computational mathematics and also in important current trends.
A3n2m Approximation Applications And Analysis Of Nonlocal Nonlinear Models
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Author : Tadele Mengesha
language : en
Publisher: Springer Nature
Release Date : 2023-09-12
A3n2m Approximation Applications And Analysis Of Nonlocal Nonlinear Models written by Tadele Mengesha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-12 with Mathematics categories.
This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.
Geometric Methods In Pde S
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Author : Giovanna Citti
language : en
Publisher: Springer
Release Date : 2015-10-31
Geometric Methods In Pde S written by Giovanna Citti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-31 with Mathematics categories.
The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications.
Fractional Calculus From Theory To Applications
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Author : Christos Volos
language : en
Publisher: BoD – Books on Demand
Release Date : 2025-05-28
Fractional Calculus From Theory To Applications written by Christos Volos and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-28 with Mathematics categories.
Over the last decade, research activity in the field of fractional calculus has surged, resulting in applications across a wide range of scientific disciplines. From the physics of diffusion and transport phenomena to control theory and financial systems, fractional calculus has proven valuable in numerous domains, capturing the interest of the scientific community. Therefore, this book comprises six chapters, each with the purpose of providing a brief overview of the subject of fractional calculus and its recent developments in theory and applications. This book aims to serve as an updated and handy reference for university professors, graduate students, laboratory researchers, as well as physicists and applied mathematicians who are interested in studying fractional calculus and its applications.
Integro Differential Elliptic Equations
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Author : Xavier Fernández-Real
language : en
Publisher: Springer Nature
Release Date : 2024-04-24
Integro Differential Elliptic Equations written by Xavier Fernández-Real and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-24 with Mathematics categories.
This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality. The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries. A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters.