Variational stabilization of degenerate p $p$ -elasticae

Abstract

A new stabilization phenomenon induced by degenerate diffusion is discovered in the context of pinned planar $p$-elasticae. It was known that in the nondegenerate regime $p\in (1,2]$, including the classical case of Euler's elastica, there are no local minimizers other than unique global minimizers. Here we prove that, in stark contrast, in the degenerate regime $p\in (2,\infty )$ there emerge uncountably many local minimizers with diverging energy.