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If we seek to find a curve y = y(x), (x1 min. while G[yn]=,y. But now the limit curve y=y0(x) must satisfy the equation G[yo] = = lim G[yn], and in order that this shall follow from the uniform convergence of yn to yo the integrand g(x, y, y') must be strongly restricted, in fact, it must be linear in y'. And, in fact, for isoperimetric problems in

Some existence theorems in the calculus of variations. II. Existence theorems for isoperimetric problems in the plane