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Harnack Inequalities And Nonlinear Operators
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Book Synopsis Harnack Inequalities and Nonlinear Operators by : Vincenzo Vespri
Download or read book Harnack Inequalities and Nonlinear Operators written by Vincenzo Vespri and published by Springer Nature. This book was released on 2021-05-29 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains two contributions about the work of Emmanuele DiBenedetto and a selection of original papers. The authors are some of the main experts in Harnack’s inequalities and nonlinear operators. These papers are part of the contributions presented during the conference to celebrate the 70th birthday of Prof. Emmanuele DiBenedetto, which was held at “Il Palazzone” in Cortona from June 18th to 24th, 2017. The papers are focused on current research topics regarding the qualitative properties of solutions, connections with calculus of variations, Harnack inequality and regularity theory. Some papers are also related to various applications. Many of the authors have shared with Prof. DiBenedetto an intense scientific and personal collaboration, while many others have taken inspiration from and further developed his field of research. The topics of the conference are certainly of great interest for the international mathematical community.
Book Synopsis The obstacle problem by : Luis Angel Caffarelli
Download or read book The obstacle problem written by Luis Angel Caffarelli and published by Edizioni della Normale. This book was released on 1999-10-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material presented here corresponds to Fermi lectures that I was invited to deliver at the Scuola Normale di Pisa in the spring of 1998. The obstacle problem consists in studying the properties of minimizers of the Dirichlet integral in a domain D of Rn, among all those configurations u with prescribed boundary values and costrained to remain in D above a prescribed obstacle F. In the Hilbert space H1(D) of all those functions with square integrable gradient, we consider the closed convex set K of functions u with fixed boundary value and which are greater than F in D. There is a unique point in K minimizing the Dirichlet integral. That is called the solution to the obstacle problem.
Book Synopsis Fully Nonlinear Elliptic Equations by : Luis A. Caffarelli
Download or read book Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on 1995 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equations, the Alexandroff estimate and Krylov-Safonov Harnack-type inequality for viscosity solutions, uniqueness theory for viscosity solutions, Evans and Krylov regularity theory for convex fully nonlinear equations, and regularity theory for fully nonlinear equations with variable coefficients.
Author :Emmanuele DiBenedetto Publisher :Springer Science & Business Media ISBN 13 :1461208955 Total Pages :402 pages Book Rating :4.4/5 (612 download)
Book Synopsis Degenerate Parabolic Equations by : Emmanuele DiBenedetto
Download or read book Degenerate Parabolic Equations written by Emmanuele DiBenedetto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolved from the author's lectures at the University of Bonn's Institut für angewandte Mathematik, this book reviews recent progress toward understanding of the local structure of solutions of degenerate and singular parabolic partial differential equations.
Book Synopsis More Progresses in Analysis by : Heinrich G. W. Begehr
Download or read book More Progresses in Analysis written by Heinrich G. W. Begehr and published by World Scientific. This book was released on 2009 with total page 1497 pages. Available in PDF, EPUB and Kindle. Book excerpt: International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.
Book Synopsis Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs by : Emanuel Indrei
Download or read book Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs written by Emanuel Indrei and published by American Mathematical Society. This book was released on 2023-01-09 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Contemporary Research in Elliptic PDEs and Related Topics by : Serena Dipierro
Download or read book Contemporary Research in Elliptic PDEs and Related Topics written by Serena Dipierro and published by Springer. This book was released on 2019-07-12 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to the Kähler-Ricci Flow by : Sebastien Boucksom
Download or read book An Introduction to the Kähler-Ricci Flow written by Sebastien Boucksom and published by Springer. This book was released on 2013-10-02 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kähler-Ricci flow and its current state-of-the-art. While several excellent books on Kähler-Einstein geometry are available, there have been no such works on the Kähler-Ricci flow. The book will serve as a valuable resource for graduate students and researchers in complex differential geometry, complex algebraic geometry and Riemannian geometry, and will hopefully foster further developments in this fascinating area of research. The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is central in G. Perelman’s celebrated proof of the Poincaré conjecture. When specialized for Kähler manifolds, it becomes the Kähler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampère equation). As a spin-off of his breakthrough, G. Perelman proved the convergence of the Kähler-Ricci flow on Kähler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelman’s ideas: the Kähler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelman’s surgeries.
Book Synopsis Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities by : Marco Bramanti
Download or read book Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities written by Marco Bramanti and published by American Mathematical Soc.. This book was released on 2010 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: "March 2010, Volume 204, number 961 (end of volume)."
Book Synopsis Fokker–Planck–Kolmogorov Equations by : Vladimir I. Bogachev
Download or read book Fokker–Planck–Kolmogorov Equations written by Vladimir I. Bogachev and published by American Mathematical Society. This book was released on 2022-02-10 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
Book Synopsis Variational Methods for Nonlocal Fractional Problems by : Giovanni Molica Bisci
Download or read book Variational Methods for Nonlocal Fractional Problems written by Giovanni Molica Bisci and published by Cambridge University Press. This book was released on 2016-03-11 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.
Book Synopsis Regularity Estimates for Nonlinear Elliptic and Parabolic Problems by : John Lewis
Download or read book Regularity Estimates for Nonlinear Elliptic and Parabolic Problems written by John Lewis and published by Springer. 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.
Book Synopsis Partial Differential Inequalities with Nonlinear Convolution Terms by : Marius Ghergu
Download or read book Partial Differential Inequalities with Nonlinear Convolution Terms written by Marius Ghergu and published by Springer Nature. This book was released on 2023-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief research monograph uses modern mathematical methods to investigate partial differential equations with nonlinear convolution terms, enabling readers to understand the concept of a solution and its asymptotic behavior. In their full generality, these inequalities display a non-local structure. Classical methods, such as maximum principle or sub- and super-solution methods, do not apply to this context. This work discusses partial differential inequalities (instead of differential equations) for which there is no variational setting. This current work brings forward other methods that prove to be useful in understanding the concept of a solution and its asymptotic behavior related to partial differential inequalities with nonlinear convolution terms. It promotes and illustrates the use of a priori estimates, Harnack inequalities, and integral representation of solutions. One of the first monographs on this rapidly expanding field, the present work appeals to graduate and postgraduate students as well as to researchers in the field of partial differential equations and nonlinear analysis.
Book Synopsis Extended Abstracts 2021/2022 by : Duván Cardona
Download or read book Extended Abstracts 2021/2022 written by Duván Cardona and published by Springer Nature. This book was released on with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Analysis on Manifolds. Monge-Ampère Equations by : Thierry Aubin
Download or read book Nonlinear Analysis on Manifolds. Monge-Ampère Equations written by Thierry Aubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is intended to allow mathematicians and physicists, especially analysts, to learn about nonlinear problems which arise in Riemannian Geometry. Analysis on Riemannian manifolds is a field currently undergoing great development. More and more, analysis proves to be a very powerful means for solving geometrical problems. Conversely, geometry may help us to solve certain problems in analysis. There are several reasons why the topic is difficult and interesting. It is very large and almost unexplored. On the other hand, geometric problems often lead to limiting cases of known problems in analysis, sometimes there is even more than one approach, and the already existing theoretical studies are inadequate to solve them. Each problem has its own particular difficulties. Nevertheless there exist some standard methods which are useful and which we must know to apply them. One should not forget that our problems are motivated by geometry, and that a geometrical argument may simplify the problem under investigation. Examples of this kind are still too rare. This work is neither a systematic study of a mathematical field nor the presentation of a lot of theoretical knowledge. On the contrary, I do my best to limit the text to the essential knowledge. I define as few concepts as possible and give only basic theorems which are useful for our topic. But I hope that the reader will find this sufficient to solve other geometrical problems by analysis.
Book Synopsis Research Topics in Analysis, Volume II by : Shouchuan Hu
Download or read book Research Topics in Analysis, Volume II written by Shouchuan Hu and published by Springer Nature. This book was released on with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Some Nonlinear Problems in Riemannian Geometry by : Thierry Aubin
Download or read book Some Nonlinear Problems in Riemannian Geometry written by Thierry Aubin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geometric and topological methods. It explores important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved.
