Diferencies ente revisiones de «Cálculu de variaciones»
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:<math>J(f_0) \-y J(f)</math>.
'''Weak''' '''maxima'''
In most problems, <math>V</math> is the space of ''r''-times [[Differentiable_function#Differentiability_classes|continuously differentiable]] functions <math>f</math> on a [[compact subset]] <math>Y</math> of the real line with n<sup>th</sup> order derivatives <math>f^{(n)}(x)</math>, and with the norm of <math>f</math> given by
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A functional <math>J</math> is said to have a '''strong minimum''' at <math>f_0</math> if there exists some <math>\delta > 0</math> such that, for all functions <math>f \neq f_0</math> with <math>\|f - f_0\|_{\infty} < \delta</math>, <math>J(f_0) < J(f)</math>. '''Strong maximum''' is defined similarly, but with the inequality in the last equation reversed.
The difference between strong and weak estrema is that, for a strong extremum, <math>f_0</math> is a local extremum relative to the set of <math>\delta</math>-close functions with respect to the supremum norm. In xeneral this (supremum) norm is different from the norm <math>\|\cdot\|_V</math> that ''V'' has been endowed with. If <math>f_0</math> is a strong extremum for <math>J</math> then it is also a weak extremum, but the parole may not hold. Finding strong estrema is more difficult than finding weak estrema and in what follows it will be assumed that we
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