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Field name	Details
Dewey Class	519
Title	Variational Methods ([EBook]) : Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems / by Michael Struwe.
Author	Struwe, Michael. , 1955-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1990.
Physical Details	XIV, 244 pages : online resource.
ISBN	9783662026243
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-02624-3
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Calculus of variations . Calculus of variations and optimal control; optimization . Dynamical Systems . Mathematical analysis . Statistical Physics . Statistical Physics, Dynamical Systems and Complexity . System theory . Systems Theory, Control . Authors: Struwe, Michael. 1955- . Struwe, Michael, 1955- . Corporate Authors: SpringerLink (Online service) . Classification: 519 .

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Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems

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