## An historical and critical study of the fundamental lemma in the calculus of variations ... |

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admissible variation analogue analytic functions arbitrary function argument assume the lemma Bois Reymond Bois Reymond's lemma Bolza calculus of variations chapter class of functions consequence of equation continuity properties continuous derivatives continuous function continuous on a,b continuous p th Crelle defined degree m-1 derivatives and vanish differential coefficients Dirksen's proof double integrals end point problem equation 1*2 equation 3-1 Euler-Lagrange equation expression finite number finite polynominal fixed end point function n(x fundamental lemma funotion gives a proof Haar Haar's theorem Heine Hence Hilbert Hobson holds integrand interior isoperimetric isoperimetric problem Kneser Kryloff Lagrange integration Legendre Legendre polynomials Mason's lemma method minimizing arc Moigno mth derivative multiple integrals number of discontinuities obtained partial derivatives polynominal of degree positive integer proof given proves the following Sarrus Stegmann Stegmann's proof sufficient surfaoe Todhunter triple integrals vanish separately variations problem involving Variationsreohnung whioh Zermelo