Diferencies ente revisiones de «Cálculu de variaciones»

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m iguo testu: estrema => divide (inglés)
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<!-- ==Weak and strong estremadivide==
A functional <math>J(f)\,</math> defined on some appropriate space of functions <math>V</math> with norm <math>\|\cdot\|_V</math> is said to have a '''weak minimum''' at the function <math>f_0</math> if there exists some <math>\delta > 0</math> such that, for all functions <math>f</math> with <math>\|f - f_0\|_V < \delta</math>,
 
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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 estremadivide 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 estremadivide is more difficult than finding weak estremadivide and in what follows it will be assumed that we are looking for weak estremadivide.
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