Regularity Of Solutions Of Fully Nonlinear Elliptic Equations
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Regularity Of Solutions Of Fully Nonlinear Elliptic Equations
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Author : Neil Sydney Trudinger
language : en
Publisher:
Release Date : 1983
Regularity Of Solutions Of Fully Nonlinear Elliptic Equations written by Neil Sydney Trudinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Fully Nonlinear Elliptic Equations
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Author : Luis A. Caffarelli
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Fully Nonlinear Elliptic Equations written by Luis A. Caffarelli 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 1995 with Mathematics categories.
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.
Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations
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Author : N. V. Krylov
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-09-07
Sobolev And Viscosity Solutions For Fully Nonlinear Elliptic And Parabolic Equations written by N. V. Krylov 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 2018-09-07 with Mathematics categories.
This book concentrates on first boundary-value problems for fully nonlinear second-order uniformly elliptic and parabolic equations with discontinuous coefficients. We look for solutions in Sobolev classes, local or global, or for viscosity solutions. Most of the auxiliary results, such as Aleksandrov's elliptic and parabolic estimates, the Krylov–Safonov and the Evans–Krylov theorems, are taken from old sources, and the main results were obtained in the last few years. Presentation of these results is based on a generalization of the Fefferman–Stein theorem, on Fang-Hua Lin's like estimates, and on the so-called “ersatz” existence theorems, saying that one can slightly modify “any” equation and get a “cut-off” equation that has solutions with bounded derivatives. These theorems allow us to prove the solvability in Sobolev classes for equations that are quite far from the ones which are convex or concave with respect to the Hessians of the unknown functions. In studying viscosity solutions, these theorems also allow us to deal with classical approximating solutions, thus avoiding sometimes heavy constructions from the usual theory of viscosity solutions.
Nonlinear Elliptic Equations And Nonassociative Algebras
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Author : Nikolai Nadirashvili
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-03
Nonlinear Elliptic Equations And Nonassociative Algebras written by Nikolai Nadirashvili 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 2014-12-03 with Mathematics categories.
This book presents applications of noncommutative and nonassociative algebras to constructing unusual (nonclassical and singular) solutions to fully nonlinear elliptic partial differential equations of second order. The methods described in the book are used to solve a longstanding problem of the existence of truly weak, nonsmooth viscosity solutions. Moreover, the authors provide an almost complete description of homogeneous solutions to fully nonlinear elliptic equations. It is shown that even in the very restricted setting of "Hessian equations", depending only on the eigenvalues of the Hessian, these equations admit homogeneous solutions of all orders compatible with known regularity for viscosity solutions provided the space dimension is five or larger. To the contrary, in dimension four or less the situation is completely different, and our results suggest strongly that there are no nonclassical homogeneous solutions at all in dimensions three and four. Thus this book gives a complete list of dimensions where nonclassical homogeneous solutions to fully nonlinear uniformly elliptic equations do exist; this should be compared with the situation of, say, ten years ago when the very existence of nonclassical viscosity solutions was not known.
Nonlinear Elliptic Equations Of The Second Order
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Author : Qing Han
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-04-15
Nonlinear Elliptic Equations Of The Second Order written by Qing Han 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 2016-04-15 with Mathematics categories.
Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler–Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge–Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and “elementary” proofs for results in important special cases. This book will serve as a valuable resource for graduate students or anyone interested in this subject.
Contributions To Nonlinear Elliptic Equations And Systems
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Author : Alexandre N. Carvalho
language : en
Publisher: Birkhäuser
Release Date : 2015-11-14
Contributions To Nonlinear Elliptic Equations And Systems written by Alexandre N. Carvalho and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-14 with Mathematics categories.
This volume of contributions pays tribute to the life and work of Djairo Guedes de Figueiredo on the occasion of his 80th birthday. The articles it contains were born out of the ICMC Summer Meeting on Differential Equations – 2014 Chapter, also dedicated to de Figueiredo and held at the Universidade de São Paulo at São Carlos, Brazil from February 3-7, 2014. The contributing authors represent a group of international experts in the field and discuss recent trends and new directions in nonlinear elliptic partial differential equations and systems. Djairo Guedes de Figueiredo has had a very active scientific career, publishing 29 monographs and over one hundred research articles. His influence on Brazilian mathematics has made him one of the pillars of the subject in that country. He had a major impact on the development of analysis, especially in its application to nonlinear elliptic partial differential equations and systems throughout the entire world. The articles collected here pay tribute to him and his legacy and are intended for graduate students and researchers in mathematics and related areas who are interested in nonlinear elliptic partial differential equations and systems.
The Abel Prize 2013 2017
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Author : Helge Holden
language : en
Publisher: Springer
Release Date : 2019-02-23
The Abel Prize 2013 2017 written by Helge Holden and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-23 with Mathematics categories.
The book presents the winners of the Abel Prize in mathematics for the period 2013–17: Pierre Deligne (2013); Yakov G. Sinai (2014); John Nash Jr. and Louis Nirenberg (2015); Sir Andrew Wiles (2016); and Yves Meyer (2017). The profiles feature autobiographical information as well as a scholarly description of each mathematician’s work. In addition, each profile contains a Curriculum Vitae, a complete bibliography, and the full citation from the prize committee. The book also includes photos for the period 2003–2017 showing many of the additional activities connected with the Abel Prize. As an added feature, video interviews with the Laureates as well as videos from the prize ceremony are provided at an accompanying website (http://extras.springer.com/). This book follows on The Abel Prize: 2003-2007. The First Five Years (Springer, 2010) and The Abel Prize 2008-2012 (Springer 2014), which profile the work of the previous Abel Prize winners.
Geometric And Analytic Aspects Of Functional Variational Principles
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Author : Rupert Frank
language : en
Publisher: Springer Nature
Release Date : 2024-11-19
Geometric And Analytic Aspects Of Functional Variational Principles written by Rupert Frank and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-19 with Mathematics categories.
This book is dedicated to exploring optimization problems of geometric-analytic nature, which are fundamental to tackling various unresolved questions in mathematics and physics. These problems revolve around minimizing geometric or analytic quantities, often representing physical energies, within prescribed collections of sets or functions. They serve as catalysts for advancing methodologies in calculus of variations, partial differential equations, and geometric analysis. Furthermore, insights from optimal functional-geometric inequalities enhance analytical problem-solving endeavors. The contributions focus on the intricate interplay between these inequalities and problems of differential and variational nature. Key topics include functional and geometric inequalities, optimal norms, sharp constants in Sobolev-type inequalities, and the regularity of solutions to variational problems. Readers will gain a comprehensive understanding of these concepts, deepening their appreciation for their relevance in mathematical and physical inquiries.
Advances In Harmonic Analysis And Partial Differential Equations
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Author : Donatella Danielli
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-04-09
Advances In Harmonic Analysis And Partial Differential Equations written by Donatella Danielli 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 2020-04-09 with Education categories.
This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Partial Differential Equations, held from April 21–22, 2018, at Northeastern University, Boston, Massachusetts. The book features a series of recent developments at the interface between harmonic analysis and partial differential equations and is aimed toward the theoretical and applied communities of researchers working in real, complex, and harmonic analysis, partial differential equations, and their applications. The topics covered belong to the general areas of the theory of function spaces, partial differential equations of elliptic, parabolic, and dissipative types, geometric optics, free boundary problems, and ergodic theory, and the emphasis is on a host of new concepts, methods, and results.
Proceedings Of The 4th European Conference Elliptic And Parabolic Problems
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Author : Josef Bemelmans
language : en
Publisher: World Scientific
Release Date : 2002
Proceedings Of The 4th European Conference Elliptic And Parabolic Problems written by Josef Bemelmans and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This book provides an overview of the state of the art in important subjects, including ? besides elliptic and parabolic issues ? geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis.