The Douglas integral can be used to solve a problem in this theory inspired by soap films.
The fundamental lemma of this theory used to transform problems from weak to strong formulations states that a certain zero functional is a convolution with the zero function. Another simplifying lemma shows that a time independent Lagrangian corresponds to a conserved energy; that identity is named for Beltrami. The Douglas integral can be used to solve a problem in this theory inspired by soap films. The central equation of this theory reduces to Lagrange's equations of motion in the limit of finitely many degrees of freedom, corresponds to seeking the stationary points of a generalized action. In additional to an early justification of Snell's Law later fashioned into Fermat's principle, problems in this branch of mathematics include showing that the cycloid solves the Brachristochrone problem. FTP, name this branch of mathematics that seeks to extremize a functional.
The fundamental lemma of this theory used to transform problems from weak to strong formulations states that a certain zero functional is a convolution with the zero function.
{Calculus} of {Variations} [accept word forms]