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Some suggestions for further study are arranged by chapter and precede the Bibliography. If the reader develops the interest to pursue some topic in one of these references, then this book will have served its purpose. These include boundary value problems for (stationary) elliptic partial differential equations and initial-boundary value problems for (time-dependent) equations of parabolic, hyperbolic, and pseudo-parabolic types. Chapter VII begins with some reflections on Chapter~III and develops into an elementary alternative treatment of certain elliptic boundary value problems by the classical Dirichlet principle. Shearer and Levy are both highly regarded researchers and educators in the field.»—David Uminsky, University of San FranciscoSubject Area:.
This chapter can be read immediately after Chapter~III and it serves as a natural place to begin work on nonlinear problems. Get Access Find out how to access preview-only content Continue reading… To view the rest of this content please follow the download PDF link above.
The latter are the Hilbert spaces in which we shall show various problems are well-posed. We use a primitive (and non-standard) notion of distribution which is adequate for our purposes. Electronic Journal of Differential Equations: Monographs Electron. J. Diff. Chapter II is an introduction to distributions and Sobolev spaces.
Get Access Find out how to access preview-only content Continue reading… To view the rest of this content please follow the download PDF link above. Non-standard items to note here are the spaces $C^m (\bar G)$, $V^*$, and $V’$. The first consists of restrictions to the closure of $G$ of functions on $R^n$ and the last two consist of conjugate-linear functionals. Preface: This book is an outgrowth of a course which we have given almost periodically over the last eight years. It is addressed to beginning graduate students of mathematics, engineering, and the physical sciences.
Also, we consider some nonlinear elliptic boundary value problems, variational or uni-lateral problems, and some methods of numerical approximation of solutions. We briefly describe the contents of the various chapters. The exercises are placed at the ends of the chapters and each is numbered so as to indicate the section for which it is appropriate. Our distributions are conjugate-linear and have the pedagogical advantage of being independent of any discussion of topological vector space theory.
Rachel Levy is associate professor of mathematics at Harvey Mudd College.
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