Minima of Invariant Functions: The Inverse Problem
We determine locally minimizing functions that are invariant with respect to the action of a finite linear group. This resolves a problem which is inverse to one discussed in a seminal paper by Abud and Sartori, and occurs naturally in various physical applications, such as elasticity theory and phase transitions. A general existence result reduces the local problem to elementary computations. Some results are extended to the compact case, and some examples and applications are given.
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