Hardcover ISBN:  9780821808573 
Product Code:  MMONO/171 
203 pp 
List Price:  $104.00 
MAA Member Price:  $93.60 
AMS Member Price:  $83.20 
Electronic ISBN:  9781470445867 
Product Code:  MMONO/171.E 
203 pp 
List Price:  $98.00 
MAA Member Price:  $88.20 
AMS Member Price:  $78.40 

Book DetailsTranslations of Mathematical MonographsVolume: 171; 1998MSC: Primary 35;
Most books on elliptic and parabolic equations emphasize existence and uniqueness of solutions. By contrast, this book focuses on the qualitative properties of solutions. In addition to the discussion of classical results for equations with smooth coefficients (Schauder estimates and the solvability of the Dirichlet problem for elliptic equations; the Dirichlet problem for the heat equation), the book describes properties of solutions to second order elliptic and parabolic equations with measurable coefficients near the boundary and at infinity.
The book presents a fine elementary introduction to the theory of elliptic and parabolic equations of second order. The precise and clear exposition is suitable for graduate students as well as for research mathematicians who want to get acquainted with this area of the theory of partial differential equations.ReadershipGraduate students and research mathematicians interested in partial differential equations and mathematical physics.

Table of Contents

Chapters

Elliptic equations in nondivergence form

Elliptic equations in divergence form

Parabolic equations


Reviews

There are probably few mathematical texts that present these deep results in such a vivid and readable manner. The book can be highly recommended to all mathematicians working in the theory of PDEs of elliptic and parabolic types. The precise and clear exposition also makes it attractive to graduate students.
European Mathematical Society Newsletter 
This book is an original and accessible account on the topics of elliptic and parabolic partial differential equations. Each section contains a number of bibliographic remarks.
Zentralblatt MATH


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Most books on elliptic and parabolic equations emphasize existence and uniqueness of solutions. By contrast, this book focuses on the qualitative properties of solutions. In addition to the discussion of classical results for equations with smooth coefficients (Schauder estimates and the solvability of the Dirichlet problem for elliptic equations; the Dirichlet problem for the heat equation), the book describes properties of solutions to second order elliptic and parabolic equations with measurable coefficients near the boundary and at infinity.
The book presents a fine elementary introduction to the theory of elliptic and parabolic equations of second order. The precise and clear exposition is suitable for graduate students as well as for research mathematicians who want to get acquainted with this area of the theory of partial differential equations.
Graduate students and research mathematicians interested in partial differential equations and mathematical physics.

Chapters

Elliptic equations in nondivergence form

Elliptic equations in divergence form

Parabolic equations

There are probably few mathematical texts that present these deep results in such a vivid and readable manner. The book can be highly recommended to all mathematicians working in the theory of PDEs of elliptic and parabolic types. The precise and clear exposition also makes it attractive to graduate students.
European Mathematical Society Newsletter 
This book is an original and accessible account on the topics of elliptic and parabolic partial differential equations. Each section contains a number of bibliographic remarks.
Zentralblatt MATH