عنوان

Variational Methods :

شابک

3662026244

شابک

9783662026243

شماره

b579223

عنوان اصلي

Variational Methods :

نام عام مواد

[Book]

ساير اطلاعات عنواني

Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

نام نخستين پديدآور

by Michael Struwe.

محل نشرو پخش و غیره

Berlin, Heidelberg

نام ناشر، پخش کننده و غيره

Springer Berlin Heidelberg

تاریخ نشرو بخش و غیره

1990

نام خاص و کميت اثر

(xiv, 244 pages)

متن يادداشت

I. The Direct Methods in the Calculus of Variations --; II. Minimax Methods --; III. Limit Cases of the Palais-Smale Condition --; Appendix A --; Sobolev Spaces --; Hölder Spaces --; Imbedding Theorems --; Density Theorem --; Trace and Extension Theorems --; Poincaré Inequality --; Appendix B --; Schauder Estimates --; Weak Solutions --; A Regularity Result --; Maximum Principle --; Weak Maximum Principle --; Application --; Appendix C --; Fréchet Differentiability --; Natural Growth Conditions --; References.

متن يادداشت

It would be hopeless to attempt to give a complete account of the history of the calculus of variations. The interest of Greek philosophers in isoperimetric problems underscores the importance of "optimal form" in ancient cultures, see Hildebrandt-Tromba [1] for a beautiful treatise of this subject. While variatio nal problems thus are part of our classical cultural heritage, the first modern treatment of a variational problem is attributed to Fermat (see Goldstine [1; p.l]). Postulating that light follows a path of least possible time, in 1662 Fer mat was able to derive the laws of refraction, thereby using methods which may already be termed analytic. With the development of the Calculus by Newton and Leibniz, the basis was laid for a more systematic development of the calculus of variations. The brothers Johann and Jakob Bernoulli and Johann's student Leonhard Euler, all from the city of Basel in Switzerland, were to become the "founding fathers" (Hildebrandt-Tromba [1; p.21]) of this new discipline. In 1743 Euler [1] sub mitted "A method for finding curves enjoying certain maximum or minimum properties", published 1744, the first textbook on the calculus of variations.

موضوع مستند نشده

Global analysis (Mathematics)

موضوع مستند نشده

Mathematics.

موضوع مستند نشده

Systems theory.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by Michael Struwe.

مستند نام اشخاص تاييد نشده

Michael Struwe

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y