Pinned planar p-elasticae

Abstract

Building on our previous work, we classify all planar $p$-elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. As an application we establish a Li--Yau type inequality for the $p$-bending energy, and in particular discover a unique exponent $p\simeq 1.5728$ for full optimality. We also prove existence of minimal $p$-elastic networks, extending a recent result of Dall'Acqua--Novaga--Pluda.

41 pages, 11 figures, final version

Cited by in corpus (3)

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• Regularity and structure of non-planar $p$-elasticae
• Variational stabilization of degenerate p-elasticae