Lectures on fully nonlinear second order elliptic equations
Author: Nikolaj N. Krylov
Publisher:
Published: 1993
Total Pages: 85
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Nikolaj N. Krylov
Publisher:
Published: 1993
Total Pages: 85
ISBN-13:
DOWNLOAD EBOOKAuthor: Nikolaĭ Vladimirovich Krylov
Publisher:
Published: 1993
Total Pages: 85
ISBN-13:
DOWNLOAD EBOOKAuthor: Luis A. Caffarelli
Publisher: American Mathematical Soc.
Published: 1995
Total Pages: 114
ISBN-13: 0821804375
DOWNLOAD EBOOKThe 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: Ya-Zhe Chen
Publisher: American Mathematical Soc.
Published: 1998
Total Pages: 266
ISBN-13: 0821819240
DOWNLOAD EBOOKThere are two parts to the book. In the first part, a complete introduction of various kinds of a priori estimate methods for the Dirichlet problem of second order elliptic partial differential equations is presented. In the second part, the existence and regularity theories of the Dirichlet problem for linear and nonlinear second order elliptic partial differential systems are introduced. The book features appropriate materials and is an excellent textbook for graduate students. The volume is also useful as a reference source for undergraduate mathematics majors, graduate students, professors, and scientists.
Author: N.N. Uraltseva
Publisher: American Mathematical Soc.
Published: 2002-04-02
Total Pages: 224
ISBN-13: 9780821896068
DOWNLOAD EBOOKThe articles in this collection present new results in partial differential equations, numerical analysis, probability theory, and geometry. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.
Author: Qing Han
Publisher: American Mathematical Soc.
Published: 2016-04-15
Total Pages: 378
ISBN-13: 1470426072
DOWNLOAD EBOOKNonlinear 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.
Author: N.V. Krylov
Publisher: Springer
Published: 2001-11-30
Total Pages: 0
ISBN-13: 9781402003349
DOWNLOAD EBOOKApproach your problems from the It isn't that they can't see the right end and begin with the solution. It is that they can't see answers. Then one day, perhaps the problem. you will find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theor.etical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.
Author: Mingxin Wang
Publisher: Springer Nature
Published:
Total Pages: 319
ISBN-13: 9819986923
DOWNLOAD EBOOKAuthor: Neil S. Trudinger
Publisher:
Published: 1995
Total Pages: 52
ISBN-13:
DOWNLOAD EBOOKAuthor: Sun-Yung A. Chang
Publisher: European Mathematical Society
Published: 2004
Total Pages: 106
ISBN-13: 9783037190067
DOWNLOAD EBOOKNon-linear elliptic partial differential equations are an important tool in the study of Riemannian metrics in differential geometry, in particular for problems concerning the conformal change of metrics in Riemannian geometry. In recent years the role played by the second order semi-linear elliptic equations in the study of Gaussian curvature and scalar curvature has been extended to a family of fully non-linear elliptic equations associated with other symmetric functions of the Ricci tensor. A case of particular interest is the second symmetric function of the Ricci tensor in dimension four closely related to the Pfaffian. In these lectures, starting from the background material, the author reviews the problem of prescribing Gaussian curvature on compact surfaces. She then develops the analytic tools (e.g., higher order conformal invariant operators, Sobolev inequalities, blow-up analysis) in order to solve a fully nonlinear equation in prescribing the Chern-Gauss-Bonnet integrand on compact manifolds of dimension four. The material is suitable for graduate students and research mathematicians interested in geometry, topology, and differential equations.