Harnack Inequalities And Nonlinear Operators

Author : Vincenzo Vespri,Ugo Gianazza,Dario Daniele Monticelli,Fabio Punzo,Daniele Andreucci
Publisher : Springer Nature
Page : 202 pages
File Size : 53,8 Mb
Release : 2021-05-29
Category : Mathematics
ISBN : 9783030737788

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Harnack Inequalities and Nonlinear Operators by Vincenzo Vespri,Ugo Gianazza,Dario Daniele Monticelli,Fabio Punzo,Daniele Andreucci Pdf

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.

Author : Serena Dipierro
Publisher : Springer
Page : 502 pages
File Size : 49,9 Mb
Release : 2019-07-12
Category : Mathematics
ISBN : 9783030189211

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Contemporary Research in Elliptic PDEs and Related Topics by Serena Dipierro Pdf

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.

Author : Emmanuele DiBenedetto,Ugo Pietro Gianazza,Vincenzo Vespri
Publisher : Springer Science & Business Media
Page : 287 pages
File Size : 44,5 Mb
Release : 2011-11-13
Category : Mathematics
ISBN : 9781461415848

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Harnack's Inequality for Degenerate and Singular Parabolic Equations by Emmanuele DiBenedetto,Ugo Pietro Gianazza,Vincenzo Vespri Pdf

Degenerate and singular parabolic equations have been the subject of extensive research for the last 25 years. Despite important achievements, the issue of the Harnack inequality for non-negative solutions to these equations, both of p-Laplacian and porous medium type, while raised by several authors, has remained basically open. Recently considerable progress has been made on this issue, to the point that, except for the singular sub-critical range, both for the p-laplacian and the porous medium equations, the theory is reasonably complete. It seemed therefore timely to trace a comprehensive overview, that would highlight the main issues and also the problems that still remain open. The authors give a comprehensive treatment of the Harnack inequality for non-negative solutions to p-laplace and porous medium type equations, both in the degenerate (p/i”2 or im/i”1) and in the singular range (1“ip/i2 or 0“im/i

Author : Marius Ghergu
Publisher : Springer Nature
Page : 141 pages
File Size : 40,9 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 9783031218569

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Partial Differential Inequalities with Nonlinear Convolution Terms by Marius Ghergu Pdf

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.

Author : Sergiu Aizicovici,Nikolaos Socrates Papageorgiou,Vasile Staicu
Publisher : American Mathematical Soc.
Page : 84 pages
File Size : 41,7 Mb
Release : 2008
Category : Differential equations, Elliptic
ISBN : 9780821841921

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Degree Theory for Operators of Monotone Type and Nonlinear Elliptic Equations with Inequality Constraints by Sergiu Aizicovici,Nikolaos Socrates Papageorgiou,Vasile Staicu Pdf

In this paper the authors examine the degree map of multivalued perturbations of nonlinear operators of monotone type and prove that at a local minimizer of the corresponding Euler functional, this degree equals one.

Author : Alberto Farina
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 53,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821848043

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Symmetry for Elliptic PDEs by Alberto Farina Pdf

Contains contributions from the INdAM School on Symmetry for Elliptic PDEs, which marked ""30 years after a conjecture of De Giorgi, and related problems"" and provided an opportunity for experts to discuss the state of the art and open questions on the subject.

Author : Feng-Yu Wang
Publisher : Springer Science & Business Media
Page : 135 pages
File Size : 47,9 Mb
Release : 2013-08-13
Category : Mathematics
ISBN : 9781461479345

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Harnack Inequalities for Stochastic Partial Differential Equations by Feng-Yu Wang Pdf

​In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

Author : Athanass Kartsatos
Publisher : CRC Press
Page : 338 pages
File Size : 40,6 Mb
Release : 1996-03-14
Category : Mathematics
ISBN : 0824797213

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Theory and Applications of Nonlinear Operators of Accretive and Monotone Type by Athanass Kartsatos Pdf

This work is based upon a Special Session on the Theory and Applications of Nonlinear Operators of Accretive and Monotone Type held during the recent meeting of the American Mathematical Society in San Francisco. It examines current developments in non-linear analysis, emphasizing accretive and monotone operator theory. The book presents a major survey/research article on partial functional differential equations with delay and an important survey/research article on approximation solvability.

Author : Bilen Emek Abali,Ivan Giorgio
Publisher : Springer Nature
Page : 484 pages
File Size : 44,6 Mb
Release : 2020-07-06
Category : Science
ISBN : 9783030504649

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Developments and Novel Approaches in Biomechanics and Metamaterials by Bilen Emek Abali,Ivan Giorgio Pdf

This book presents a selection of cutting-edge methods that allow readers to obtain novel models for nonlinear solid mechanics. Today, engineers need more accurate techniques for modeling solid body mechanics, chiefly due to innovative methods like additive manufacturing—for example, 3D printing—but also due to miniaturization. This book focuses on the formulation of continuum and discrete models for complex materials and systems, and especially the design of metamaterials. It gathers outstanding papers from the international conference IcONSOM 2019

Author : Emmanuele DiBenedetto,Ugo Gianazza
Publisher : Springer Nature
Page : 768 pages
File Size : 53,9 Mb
Release : 2023
Category : Differential equations, Partial
ISBN : 9783031466182

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Partial Differential Equations by Emmanuele DiBenedetto,Ugo Gianazza Pdf

This graduate textbook provides a self-contained introduction to the classical theory of partial differential equations (PDEs). Through its careful selection of topics and engaging tone, readers will also learn how PDEs connect to cutting-edge research and the modeling of physical phenomena. The scope of the Third Edition greatly expands on that of the previous editions by including five new chapters covering additional PDE topics relevant for current areas of active research. This includes coverage of linear parabolic equations with measurable coefficients, parabolic DeGiorgi classes, Navier-Stokes equations, and more. The “Problems and Complements” sections have also been updated to feature new exercises, examples, and hints toward solutions, making this a timely resource for students. Partial Differential Equations: Third Edition is ideal for graduate students interested in exploring the theory of PDEs and how they connect to contemporary research. It can also serve as a useful tool for more experienced readers who are looking for a comprehensive reference.

Author : Gui-Qiang Chen,Emmanuele DiBenedetto
Publisher : American Mathematical Soc.
Page : 323 pages
File Size : 40,8 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821811962

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Nonlinear Partial Differential Equations by Gui-Qiang Chen,Emmanuele DiBenedetto Pdf

This volume is a collection of original research papers and expository articles stemming from the scientific program of the Nonlinear PDE Emphasis Year held at Northwestern University (Evanston, IL) in March 1998. The book offers a cross-section of the most significant recent advances and current trends and directions in nonlinear partial differential equations and related topics. The book's contributions offer two perspectives. There are papers on general analytical treatment of the theory and papers on computational methods and applications originating from significant realistic mathematical models of natural phenomena. Also included are articles that bridge the gap between these two perspectives, seeking synergistic links between theory and modeling and computation. The volume offers direct insight into recent trends in PDEs. This volume is also available on the Web. Those who purchase the print edition can gain free access by going to www.ams.org/conm/.

Author : Marco Bramanti
Publisher : American Mathematical Soc.
Page : 136 pages
File Size : 53,8 Mb
Release : 2010
Category : Differential inequalities
ISBN : 9780821849033

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Non-Divergence Equations Structured on Hormander Vector Fields: Heat Kernels and Harnack Inequalities by Marco Bramanti Pdf

"March 2010, Volume 204, number 961 (end of volume)."

Author : Heinrich G. W. Begehr,Francesco Nicolosi
Publisher : World Scientific
Page : 1497 pages
File Size : 48,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812835628

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More Progresses in Analysis by Heinrich G. W. Begehr,Francesco Nicolosi Pdf

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.

Author : Edgard A. Pimentel
Publisher : Cambridge University Press
Page : 204 pages
File Size : 50,5 Mb
Release : 2022-06-30
Category : Mathematics
ISBN : 9781009103121

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Elliptic Regularity Theory by Approximation Methods by Edgard A. Pimentel Pdf

Presenting the basics of elliptic PDEs in connection with regularity theory, the book bridges fundamental breakthroughs – such as the Krylov–Safonov and Evans–Krylov results, Caffarelli's regularity theory, and the counterexamples due to Nadirashvili and Vlăduţ – and modern developments, including improved regularity for flat solutions and the partial regularity result. After presenting this general panorama, accounting for the subtleties surrounding C-viscosity and Lp-viscosity solutions, the book examines important models through approximation methods. The analysis continues with the asymptotic approach, based on the recession operator. After that, approximation techniques produce a regularity theory for the Isaacs equation, in Sobolev and Hölder spaces. Although the Isaacs operator lacks convexity, approximation methods are capable of producing Hölder continuity for the Hessian of the solutions by connecting the problem with a Bellman equation. To complete the book, degenerate models are studied and their optimal regularity is described.

Author : Xavier Fernández-Real
Publisher : Springer Nature
Page : 409 pages
File Size : 42,8 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9783031542428

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Integro-Differential Elliptic Equations by Xavier Fernández-Real Pdf