The Weierstrass 𝐸-function in the calculus of variations
1946; American Mathematical Society; Volume: 60; Linguagem: Inglês
10.1090/s0002-9947-1946-0017478-x
ISSN1088-6850
Autores Tópico(s)Matrix Theory and Algorithms
ResumoThe fupnctions cf/, fo, f are positively homogeneous in the variables yi. The problem here formulated contains as special cases most of the interesting problems in the calculus of variations involving simple integrals('). In the present paper we shall develop certain interesting properties of the Weierstrass E-function. These properties are of interest apart from their applications to be found in the papers that follow. We shall be concerned particularly with the concept of E-dominance. This concept can be described briefly as follows: Let Z be the set of all admissible elements (a, y, p) satisfying the conditions q5A(a, y, p) =0 and let Co be an arc whose elements (a, y, p) = (a, y, y) are in Z. A function F(a, y, p) will be said to E-dominate a second function H(a, y, p) near Co on Z if there is a neighborhood Zo relative to Z of the elements (a, y, p) on CO and a constant b >0 such that the inequality
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