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I am currently studying GMT and a topic that has popped up in the course is the use of calibrations as a tool for proving that a particular set $E$ attains the minimum for the problem

$$min \left \lbrace P(A) + \int_{A} f \right \rbrace$$

We said that, basically, if you can find a function $g$ with some properties (which is called a calibration for $E$) then $E$ is a global minimum for the above minimization problem. We also saw some examples and briefly talked about local minima, but there are some things I don't get about those. That is why I was looking for some books, notes, anything that explains this method with some examples to understand better and look at this topic more in detail, but I couldn't find anything, every book I checked doesn't talk about this at all, or if it does it's basically a remark. Do you know about anything with more explanations about this? If there were carried out examples it would be perfect.

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  • $\begingroup$ What books have you checked? $\endgroup$
    – Leo Moos
    Commented Aug 19, 2022 at 20:20
  • $\begingroup$ Federer, Simon, Evans-Gariepy, Maggi, Ambrosio-Fusco-Pallara, Morgan $\endgroup$
    – tommy1996q
    Commented Aug 20, 2022 at 16:09
  • $\begingroup$ It looks like you've covered the main ones... Although Chapter 6 in Morgan and Sections 5.4.18-19 in Federer do talk about calibrations a bit. Why don't you ask your prof? I am sure they'd be happy to recommend some further reading. $\endgroup$
    – Leo Moos
    Commented Aug 20, 2022 at 22:52
  • $\begingroup$ Yeah I guess I will. I'll just wait until September, just to let summer end $\endgroup$
    – tommy1996q
    Commented Aug 20, 2022 at 23:16

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