Direct Methods in the Theory of Elliptic Equations

出版者:Springer

作者:Jindrich Necas

页数:388

译者:Alois Kufner

出版时间:2012-3-5

价格:USD 129.00

装帧:Hardcover

isbn号码:9783642104541

丛书系列:Springer Monographs in Mathematics

图书标签:数学SpringerPDE2012

Necas's famous book Direct methods in the theory of elliptic equations has become standard reference material on the mathematical theory of linear elliptic equations and systems, and also on the related function spaces framework. It provides a concise and self-contained introduction to the modern theory of partial differential equations, the theory of weak solutions and related topics. It is recommended to scientists working in the field of partial differential equations, postgraduate and graduate students, and applied mathematicians. The first chapter is devoted to directs methods, introduction to the Sobolev spaces, weak solution, Lax-Milgram theorem, Galerkin metods and spectral theory. The second chapter deals with the basic properties of Sobolev spaces (imbeddings, traces, compact imbeddings, fractional spaces).The third chapter contains existence and uniqueness theorems for problems, including the Fredholm alternative and systems of equations with variable coefficients. The next chapter describes regularity properties of weak solutions. Chapter 5 deals with applications of Rellich's inequality and Chapter 6 introduces the Sobolev spaces with weights. Finally the last chapter studies regularity of solutions and their dependence on coefficients and also on irregular domains.