In mathematics, the direct method in the calculus of variations is a general method for constructing a proof of the existence of a minimizer for a given...

The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and...

magnitudes Direct method in calculus of variations for constructing a proof of the existence of a minimizer for a given functional Direct method (accounting)...

In the calculus of variations, a subfield of mathematics, quasiconvexity is a generalisation of the notion of convexity. It is used to characterise the...

Riemann's use of Dirichlet's principle by developing the direct method in the calculus of variations. Dirichlet problem Hilbert's twentieth problem Plateau's...

a variation of Fubini's theorem, and for introducing semicontinuity methods as a common tool for the direct method in the calculus of variations. Tonelli...

derivatives and the geometry of its domain of definition. Such bounds are of great importance in the modern, direct methods of the calculus of variations. A very...

A variational principle is a mathematical procedure that renders a physical problem solvable by the calculus of variations, which concerns finding functions...

using the calculus of variations (hence the name "variational Bayes") that the "best" distribution q j ∗ {\displaystyle q_{j}^{*}} for each of the factors...

Weierstrass. Much later, in 1900, Hilbert justified Riemann's approach by developing the direct method in the calculus of variations. In the 1860s and 1870s,...

of calculus, the other being integral calculus—the study of the area beneath a curve. The primary objects of study in differential calculus are the derivative...

to prove that it is analytic. On the other hand, direct methods in the calculus of variations showed the existence of solutions with very weak differentiability...

flaw in Riemann's argument, and a rigorous proof of existence was found only in 1900 by David Hilbert, using his direct method in the calculus of variations...

In the calculus of variations, the notion of polyconvexity is a generalization of the notion of convexity for functions defined on spaces of matrices....

invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and...

tools from the calculus of variations and optimal control. The curve is independent of both the mass of the test body and the local strength of gravity....

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at every...

calculus, calculus of variations, lambda calculus, sequent calculus, and process calculus. Furthermore, the term "calculus" has variously been applied in ethics...

theorem of calculus Integration by parts Inverse chain rule method Integration by substitution Tangent half-angle substitution Differentiation under the integral...

setting for the theory of partial differential equations. They also form the basis of the theory of direct methods in the calculus of variations. For s a...

contributions to the calculus of variations and the theory of partial differential equations. Charles Bradfield Morrey Jr. was born July 23, 1907, in Columbus...

stochastic calculus are the Itô calculus and its variational relative the Malliavin calculus. For technical reasons the Itô integral is the most useful...

had begun working on a form of calculus (which he called "The Method of Fluxions and Infinite Series") in 1666, at the age of 23, but did not publish it...

related to the calculus of residues, a method of complex analysis. One use for contour integrals is the evaluation of integrals along the real line that...

In the calculus of variations, a branch of mathematics, a Nehari manifold is a manifold of functions, whose definition is motivated by the work of Zeev...

fundamental theorem of calculus relates definite integration to differentiation and provides a method to compute the definite integral of a function when...

experimented with soap films. The problem is considered part of the calculus of variations. The existence and regularity problems are part of geometric measure theory...

1863 in Romanówka, present-day Ukraine. The son of an engineer, he was educated at a grammar school in Saint Petersburg and studied at the Institute of Technology...

the existence of solutions to variational problems when classical direct methods of the calculus of variations cannot be applied. In particular, the so-called...

their inception. In 1993, Moore employed a numerical implementation of the direct method from the calculus of variations to uncover the "eight" choreography...