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基本説明
From the reviews - The principal theme of this book is the existence and differentiability of solutions of variational problems involving multiple integrals. - M. R. Hestenes in Journal of Optimization Theory and Applications
Full Description
From the reviews: "...the book contains a wealth of material essential to the researcher concerned with multiple integral variational problems and with elliptic partial differential equations. The book not only reports the researches of the author but also the contributions of his contemporaries in the same and related fields. The book undoubtedly will become a standard reference for researchers in these areas. ...The book is addressed mainly to mature mathematical analysts. However, any student of analysis will be greatly rewarded by a careful study of this book."
M. R. Hestenes in Journal of Optimization Theory and Applications
"The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems."
L. Schmetterer in Monatshefte für Mathematik
"The book is very clearly exposed and contains the last modern theory in this domain. A comprehensive bibliography ends the book."
M. Coroi-Nedeleu in Revue Roumaine de Mathématiques Pures et Appliquées
Contents
Semi-classical results.- The spaces Hmp and Hmp0.- Existence theorems.- Differentiability of weak solutions.- Regularity theorems for the solutions of general elliptic systems and boundary value problems.- A variational method in the theory of harmonic integrals.- The -Neumann problem on strongly pseudo-convex manifolds.- to parametric Integrals; two dimensional problems.- The higher dimensional plateau problems.
