Linear and nonlinear perturbations of the operator div
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Bibliographic Information
Linear and nonlinear perturbations of the operator div
（Translations of mathematical monographs, v. 160）
American Mathematical Society, c1997
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Линейные и нелинейые возмущения оператора div
Lineĭnye i nelineĭye vozmushchenii︠a︡ operatora div
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Note
Translation of: Линейные и нелинейые возмущения оператора div. Санкт-Петербург : Изд-во. Петербургского унив., 1995
Includes bibliographical references
Description and Table of Contents
Description
The perturbation theory for the operator div is of particular interest in the study of boundary-value problems for the general nonlinear equation $F(\dot y,y,x)=0$. Taking as linearization the first order operator $Lu=C_{ij}u_{x_j}^i+C_iu^i$, one can, under certain conditions, regard the operator $L$ as a compact perturbation of the operator div. This book presents results on boundary-value problems for $L$ and the theory of nonlinear perturbations of $L$. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator $L$. An analog of the Weyl decomposition is proved.The book also contains a local description of the set of all solutions (located in a small neighborhood of a known solution) to the boundary-value problems for the nonlinear equation $F(\dot y, y, x) = 0$ for which $L$ is a linearization. A classification of sets of all solutions to various boundary-value problems for the nonlinear equation $F(\dot y, y, x) = 0$ is given. The results are illustrated by various applications in geometry, the calculus of variations, physics, and continuum mechanics.
Table of Contents
Notation Linear perturbations of the operator div Nonlinear perturbations of the operator div Appendix References.
by "Nielsen BookData"