FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2184175071> ?p ?o ?g. }

• W2184175071 abstract "Minimization principles form one of the most wide-ranging means of formulating mathematical models governing the equilibrium configurations of physical systems. Moreover, many popular numerical integration schemes such as the powerful finite element method are also founded upon a minimization paradigm. In these notes, we will develop the basic mathematical analysis of nonlinear minimization principles on infinite-dimensional function spaces — a subject known as the “calculus of variations”, for reasons that will be explained as soon as we present the basic ideas. Classical solutions to minimization problems in the calculus of variations are prescribed by boundary value problems involving certain types of differential equations, known as the associated Euler–Lagrange equations. The mathematical techniques that have been developed to handle such optimization problems are fundamental in many areas of mathematics, physics, engineering, and other applications. In this chapter, we will only have room to scratch the surface of this wide ranging and lively area of both classical and contemporary research. The history of the calculus of variations is tightly interwoven with the history of mathematics. The field has drawn the attention of a remarkable range of mathematical luminaries, beginning with Newton, then initiated as a subject in its own right by the Bernoulli family. The first major developments appeared in the work of Euler, Lagrange and Laplace. In the nineteenth century, Hamilton, Dirichlet and Hilbert are but a few of the outstanding contributors. In modern times, the calculus of variations has continued to occupy center stage, witnessing major theoretical advances, along with wide-ranging applications in physics, engineering and all branches of mathematics. Minimization problems that can be analyzed by the calculus of variations serve to characterize the equilibrium configurations of almost all continuous physical systems, ranging through elasticity, solid and fluid mechanics, electro-magnetism, gravitation, quantum mechanics, string theory, and many, many others. Many geometrical configurations, such as minimal surfaces, can be conveniently formulated as optimization problems. Moreover, numerical approximations to the equilibrium solutions of such boundary value problems are based on a nonlinear finite element approach that reduces the infinite-dimensional minimization problem to a finite-dimensional problem. See [12; Chapter 11] for full details. Just as the vanishing of the gradient of a function of several variables singles out the critical points, among which are the minima, both local and global, so a similar “functional gradient” will distinguish the candidate functions that might be minimizers of the functional. The finite-dimensional calculus leads to a system of algebraic equations for the critical points; the infinite-dimensional functional analog results a boundary value problem for a nonlinear ordinary or partial differential equation whose solutions are the critical" @default.
• W2184175071 created "2016-06-24" @default.
• W2184175071 creator A5070840504 @default.
• W2184175071 date "2014-01-01" @default.
• W2184175071 modified "2023-10-10" @default.
• W2184175071 title "Introduction to the Calculus of Variations" @default.
• W2184175071 cites W1508861003 @default.
• W2184175071 cites W1535448269 @default.
• W2184175071 cites W1565212980 @default.
• W2184175071 cites W1666853924 @default.
• W2184175071 cites W2007626594 @default.
• W2184175071 cites W2059327787 @default.
• W2184175071 cites W2113741845 @default.
• W2184175071 cites W2123354485 @default.
• W2184175071 cites W2157715842 @default.
• W2184175071 cites W2318401074 @default.
• W2184175071 cites W2324087097 @default.
• W2184175071 cites W378485725 @default.
• W2184175071 hasPublicationYear "2014" @default.
• W2184175071 type Work @default.
• W2184175071 sameAs 2184175071 @default.
• W2184175071 citedByCount "0" @default.
• W2184175071 countsByYear W21841750712021 @default.
• W2184175071 crossrefType "journal-article" @default.
• W2184175071 hasAuthorship W2184175071A5070840504 @default.
• W2184175071 hasConcept C126255220 @default.
• W2184175071 hasConcept C134306372 @default.
• W2184175071 hasConcept C147764199 @default.
• W2184175071 hasConcept C159985019 @default.
• W2184175071 hasConcept C192562407 @default.
• W2184175071 hasConcept C199343813 @default.
• W2184175071 hasConcept C204323151 @default.
• W2184175071 hasConcept C2777686260 @default.
• W2184175071 hasConcept C28826006 @default.
• W2184175071 hasConcept C33923547 @default.
• W2184175071 hasConcept C71924100 @default.
• W2184175071 hasConcept C97985569 @default.
• W2184175071 hasConceptScore W2184175071C126255220 @default.
• W2184175071 hasConceptScore W2184175071C134306372 @default.
• W2184175071 hasConceptScore W2184175071C147764199 @default.
• W2184175071 hasConceptScore W2184175071C159985019 @default.
• W2184175071 hasConceptScore W2184175071C192562407 @default.
• W2184175071 hasConceptScore W2184175071C199343813 @default.
• W2184175071 hasConceptScore W2184175071C204323151 @default.
• W2184175071 hasConceptScore W2184175071C2777686260 @default.
• W2184175071 hasConceptScore W2184175071C28826006 @default.
• W2184175071 hasConceptScore W2184175071C33923547 @default.
• W2184175071 hasConceptScore W2184175071C71924100 @default.
• W2184175071 hasConceptScore W2184175071C97985569 @default.
• W2184175071 hasLocation W21841750711 @default.
• W2184175071 hasOpenAccess W2184175071 @default.
• W2184175071 hasPrimaryLocation W21841750711 @default.
• W2184175071 hasRelatedWork W1019198162 @default.
• W2184175071 hasRelatedWork W157614816 @default.
• W2184175071 hasRelatedWork W1820125862 @default.
• W2184175071 hasRelatedWork W1937143166 @default.
• W2184175071 hasRelatedWork W2021956773 @default.
• W2184175071 hasRelatedWork W2068847270 @default.
• W2184175071 hasRelatedWork W2109865933 @default.
• W2184175071 hasRelatedWork W2133104409 @default.
• W2184175071 hasRelatedWork W2133770547 @default.
• W2184175071 hasRelatedWork W2310237 @default.
• W2184175071 hasRelatedWork W239394738 @default.
• W2184175071 hasRelatedWork W2482901637 @default.
• W2184175071 hasRelatedWork W2503659851 @default.
• W2184175071 hasRelatedWork W2738710098 @default.
• W2184175071 hasRelatedWork W2949128074 @default.
• W2184175071 hasRelatedWork W2991335284 @default.
• W2184175071 hasRelatedWork W3014886719 @default.
• W2184175071 hasRelatedWork W594157154 @default.
• W2184175071 hasRelatedWork W644903696 @default.
• W2184175071 hasRelatedWork W88531024 @default.
• W2184175071 isParatext "false" @default.
• W2184175071 isRetracted "false" @default.
• W2184175071 magId "2184175071" @default.
• W2184175071 workType "article" @default.