Variational stabilization of degenerate 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 non-degenerate 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.

23 pages, 3 figures, final version

References in corpus (6)

• Generalized elliptic functions and their application to a nonlinear eigenvalue problem with $p$-Laplacian
• Convergence of elastic flows of curves into manifolds
• Elastic curves and phase transitions
• Li-Yau type inequality for curves in any codimension
• On the isoperimetric inequality and surface diffusion flow for multiply winding curves
• Pinned planar p-elasticae