Category

Calculus of variations

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calculus of variations

differential calculus on function spaces

Fermat's principle

principle of least time

Noether's theorem

physical law that differentiable symmetries correspond to conservation laws

physical quantity of dimension energy × time

Euler–Lagrange equation

second-order partial differential equation whose solutions are the functions for which a given functional is stationary

Hamilton's principle

principle that the dynamics of a physical system are determined by a variational problem of the Lagrangian

isoperimetric inequality

geometric inequality which sets a lower bound on the surface area of a set given its volume

functional of dynamical variables whose variation yields the equations of motion in Lagrangian mechanics

transportation theory

the mathematical study of optimal transportation and allocation of resources

variational principle

a scientific principle used within the calculus of variations, which develops general methods for finding functions which extremize the value of quantities that depend upon those functions

Dirichlet's principle

concept in potential theory

function of bounded variation

real function with finite total variation

functional derivative

concept in calculus of variation

Plateau's problem

in calculus of variations, the problem proving the existence of a minimal surface with a given boundary

Brunn–Minkowski theorem

theorem in geometry

fundamental lemma of calculus of variations

initial result in using test functions to find extremum

geometric analysis

mathematical discipline at the interface of differential geometry and differential equations

Malliavin calculus

mathematical techniques used in probability theory and related fields

Stampacchia Medal

envelope theorem

theorem in mathematics and economics

Noether's second theorem

Physics theorem for symmetries of action

Dirichlet's energy

half of the integral of the squared gradient of a function on its domain

Maupertuis's principle

principle of least length in physics

geodesics on an ellipsoid

shortest paths on a bounded deformed sphere-like quadric surface

Hilbert's twenty-third problem

Promotes work on calculus of variations

Hilbert's nineteenth problem

one of the 23 Hilbert problems

Hilbert's twentieth problem

Can all boundary value problems be solved

Morse–Palais lemma

theorem that a smooth enough function near a critical point can be expressed as a quadratic form after a suitable change of coordinates

Beltrami identity

special case of the Euler-Lagrange equation