Lectures On Elliptic And Parabolic Equations In H Lder Spaces
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Lectures On Elliptic And Parabolic Equations In Holder Spaces
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Author : Nikolaĭ Vladimirovich Krylov
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Lectures On Elliptic And Parabolic Equations In Holder Spaces written by Nikolaĭ Vladimirovich 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 1996 with Mathematics categories.
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.
Partial Differential Equations For Probabalists Sic
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Author : Daniel W. Stroock
language : en
Publisher: Cambridge University Press
Release Date : 2008
Partial Differential Equations For Probabalists Sic written by Daniel W. Stroock and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Differential equations, Elliptic categories.
Kolmogorov's forward, basic results -- Non-elliptic regularity results -- Preliminary elliptic regularity results -- Nash theory -- Localization -- On a manifold -- Subelliptic estimates and Hörmander's theorem.
Lectures On Elliptic And Parabolic Equations In Hlder Spaces
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Author : Nikolaj Valdimirovich Krylov
language : de
Publisher:
Release Date : 1996
Lectures On Elliptic And Parabolic Equations In Hlder Spaces written by Nikolaj Valdimirovich Krylov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Approximation Methods And Analytical Modeling Using Partial Differential Equations
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Author : Tamara Fastovska
language : en
Publisher: Frontiers Media SA
Release Date : 2025-03-28
Approximation Methods And Analytical Modeling Using Partial Differential Equations written by Tamara Fastovska and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-28 with Science categories.
Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. As soon as an appropriate mathematical model is developed, it can be comprehensively analyzed by a broad spectrum of available mathematical methods. For example, compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases and in mathematical models of population genetics. While the existence of an optimal solution under certain condition can be often proved rigorously, this does not always mean that such a solution is easy to implement in practice. Finding a reasonable approximation can in itself be a challenging research problem. This Research Topic is devoted to modeling, analysis, and approximation problems whose solutions exploit and explore the theory of partial differential equations. It aims to highlight new analytical tools for use in the modeling of problems arising in applied sciences and practical areas. Researchers are invited to submit articles that investigate the qualitative behavior of weak solutions (removability conditions for singularities), the dependence of the local asymptotic property of these solutions on initial and boundary data, and also the existence of solutions. Contributors are particularly encouraged to focus on anisotropic models: analyzing the preconditions on the strength of the anisotropy, and comparing the analytical estimates for the growth behavior of the solutions near the singularities with the observed growth in numerical simulations. The qualitative analysis and analytical results should be confirmed by the numerically observed solution behavior.
Lectures On Elliptic And Parabolic Equations In Sobolev Spaces
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Author : Nikolaĭ Vladimirovich Krylov
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Lectures On Elliptic And Parabolic Equations In Sobolev Spaces written by Nikolaĭ Vladimirovich 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 2008 with Mathematics categories.
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.
Lectures On Elliptic And Parabolic Equations In Sobolev Spaces
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Author : N. V. Krylov
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-31
Lectures On Elliptic And Parabolic Equations In Sobolev Spaces written by N. V. Krylov and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-31 with Mathematics categories.
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 $mathsf{VMO}$ 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. Prerequisites are basics of measure theory, the theory of $L_p$ spaces, and the Fourier transform.
Heisenberg Calculus And Spectral Theory Of Hypoelliptic Operators On Heisenberg Manifolds
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Author : Raphael Ponge
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Heisenberg Calculus And Spectral Theory Of Hypoelliptic Operators On Heisenberg Manifolds written by Raphael Ponge 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 2008 with Mathematics categories.
This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.
Lectures On Elliptic And Parabolic Equations In H Lder Spaces
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Author : Nikolaĭ Vladimirovich Krylov
language : en
Publisher:
Release Date : 1900
Lectures On Elliptic And Parabolic Equations In H Lder Spaces written by Nikolaĭ Vladimirovich Krylov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1900 with Differential equations, Elliptic categories.
Hilbert Space Methods In Partial Differential Equations
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Author : Ralph E. Showalter
language : en
Publisher: Courier Corporation
Release Date : 2011-09-12
Hilbert Space Methods In Partial Differential Equations written by Ralph E. Showalter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-12 with Mathematics categories.
This graduate-level text opens with an elementary presentation of Hilbert space theory sufficient for understanding the rest of the book. Additional topics include boundary value problems, evolution equations, optimization, and approximation.1979 edition.
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.