Hardcover ISBN:  9783037190425 
Product Code:  EMSTEXT/4 
List Price:  $68.00 
AMS Member Price:  $54.40 

Book DetailsEMS Textbooks in MathematicsVolume: 4; 2007; 303 ppMSC: Primary 35; 46; 42; 47;
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 nspace, including a priori estimates for boundaryvalue 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 LaplacePoisson 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 twosemester 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.ReadershipGraduate students and research mathematicians interested in differential equations and analysis.

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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 nspace, including a priori estimates for boundaryvalue 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 LaplacePoisson 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 twosemester 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.
Graduate students and research mathematicians interested in differential equations and analysis.