Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Lectures On Elliptic And Parabolic Equations In Sobolev Spaces PDF full book. Access full book title Lectures On Elliptic And Parabolic Equations In Sobolev Spaces.
| Author | : Nikolaĭ Vladimirovich Krylov |
| Publisher | : |
| Total Pages | : 377 |
| Release | : 1900 |
| Genre | : Differential equations, Elliptic |
| ISBN | : 9781470421212 |
| Author | : Nikolaĭ Vladimirovich Krylov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 377 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821846841 |
This book concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations. In addition, other boundary-value problems such as the Neumann or oblique derivative problems are briefly covered. As is natural for a textbook, the main emphasis is on organizing well-known ideas in a self-contained exposition. Among the topics included that are not usually covered in a textbook are a relatively recent development concerning equations with $\textsf{VMO}$ coefficients and the study of parabolic equations with coefficients measurable only with respect to the time variable. There are numerous exercises which help the reader better understand the material. After going through the book, the reader will have a good understanding of results available in the modern theory of partial differential equations and the technique used to obtain them. Prerequesites are basics of measure theory, the theory of $L p$ spaces, and the Fourier transform.
| Author | : Nikolaĭ Vladimirovich Krylov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 1996 |
| Genre | : Mathematics |
| ISBN | : 082180569X |
These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, containing 200 exercises, aims to provide a good understanding of what kind of results are available and what kinds of techniques are used to obtain them.
| Author | : Vladimir Maz'ya |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 882 |
| Release | : 2011-02-11 |
| Genre | : Mathematics |
| ISBN | : 3642155642 |
Sobolev spaces play an outstanding role in modern analysis, in particular, in the theory of partial differential equations and its applications in mathematical physics. They form an indispensable tool in approximation theory, spectral theory, differential geometry etc. The theory of these spaces is of interest in itself being a beautiful domain of mathematics. The present volume includes basics on Sobolev spaces, approximation and extension theorems, embedding and compactness theorems, their relations with isoperimetric and isocapacitary inequalities, capacities with applications to spectral theory of elliptic differential operators as well as pointwise inequalities for derivatives. The selection of topics is mainly influenced by the author’s involvement in their study, a considerable part of the text is a report on his work in the field. Part of this volume first appeared in German as three booklets of Teubner-Texte zur Mathematik (1979, 1980). In the Springer volume “Sobolev Spaces”, published in English in 1985, the material was expanded and revised. The present 2nd edition is enhanced by many recent results and it includes new applications to linear and nonlinear partial differential equations. New historical comments, five new chapters and a significantly augmented list of references aim to create a broader and modern view of the area.
| Author | : Mikhail S. Agranovich |
| Publisher | : Springer |
| Total Pages | : 343 |
| Release | : 2015-05-06 |
| Genre | : Mathematics |
| ISBN | : 3319146483 |
This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.
| Author | : Luigi Ambrosio |
| Publisher | : Springer |
| Total Pages | : 230 |
| Release | : 2019-01-10 |
| Genre | : Mathematics |
| ISBN | : 8876426515 |
The book originates from the Elliptic PDE course given by the first author at the Scuola Normale Superiore in recent years. It covers the most classical aspects of the theory of Elliptic Partial Differential Equations and Calculus of Variations, including also more recent developments on partial regularity for systems and the theory of viscosity solutions.
| Author | : N.V. Krylov |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2001-11-30 |
| Genre | : Mathematics |
| ISBN | : 9781402003349 |
Approach 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 | : Zhuoqun Wu |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 425 |
| Release | : 2006-10-17 |
| Genre | : Mathematics |
| ISBN | : 9813101709 |
This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them.
| Author | : Dorothee Haroske |
| Publisher | : European Mathematical Society |
| Total Pages | : 312 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 9783037190425 |
It is the main aim of this book to develop at an accessible, moderate level an $L_2$ theory for elliptic differential operators of second order on bounded smooth domains in Euclidean n-space, including a priori estimates for boundary-value problems in terms of (fractional) Sobolev spaces on domains and on their boundaries, together with a related spectral theory. The presentation is preceded by an introduction to the classical theory for the Laplace-Poisson equation, and some chapters provide required ingredients such as the theory of distributions, Sobolev spaces and the spectral theory in Hilbert spaces. The book grew out of two-semester courses the authors have given several times over a period of ten years at the Friedrich Schiller University of Jena. It is addressed to graduate students and mathematicians who have a working knowledge of calculus, measure theory and the basic elements of functional analysis (as usually covered by undergraduate courses) and who are seeking an accessible introduction to some aspects of the theory of function spaces and its applications to elliptic equations.
| Author | : Nikolaĭ Vladimirovich Krylov |
| Publisher | : |
| Total Pages | : 166 |
| Release | : 1900 |
| Genre | : Differential equations, Elliptic |
| ISBN | : 9781470420703 |
