Lectures on Elliptic and Parabolic Equations in Holder Spaces

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Overview

These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in Holder 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, with nearly 200 exercises, will provide a good understanding of what kinds of results are available and what kinds of techniques are used to obtain them.

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Editorial Reviews

Booknews
Describes the fundamentals of the title theory, for graduate students and researchers in mathematics, physics, and engineering. The main focus is on first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative. Also discusses numerical approximations. Includes nearly 200 exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780821805695
  • Publisher: American Mathematical Society
  • Publication date: 9/1/1996
  • Series: Graduate Studies in Mathematics Series , #12
  • Pages: 164
  • Product dimensions: 7.20 (w) x 10.20 (h) x 0.60 (d)

Table of Contents

Preface
Ch. 1 Elliptic Equations with Constant Coefficients in R[superscript d] 1
Ch. 2 Laplace's Equation 15
Ch. 3 Solvability of Elliptic Equations with Constant Coefficients in the Holder Spaces 33
Ch. 4 Elliptic Equations with Variable Coefficients in R[superscript d] 51
Ch. 5 Second-Order Elliptic Equations in Half Spaces 65
Ch. 6 Second-Order Elliptic Equations in Smooth Domains 77
Ch. 7 Elliptic Equations in Non-Smooth Domains 91
Ch. 8 Parabolic Equations in the Whole Space 105
Ch. 9 Boundary-Value Problems for Parabolic Equations in Half Spaces 137
Ch. 10 Parabolic Equations in Domains 147
Bibliography 161
Index 163
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