If we have a function f that has a minimum at a point say x. Does f preserve the min if we convolve it with a mollifier?
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closed as too localized by Harald HancheOlsen, Willie Wong, Deane Yang, S. Carnahan♦ Nov 8 '10 at 2:24This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question. 


No, consider a function $f$ with a graph something like the above for example. (Pardon the rough sketch:) When you mollify it the minimum at the origin will rise and become greater that the value of the mollified function away from the origin. 

