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arXiv · 2209.05721

Pinned planar p-elasticae

Tatsuya Miura·Kensuke Yoshizawa
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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.

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Tatsuya Miura, Kensuke Yoshizawa. 2022-09-13. Pinned planar p-elasticae. https://doi.org/10.1512/iumj.2024.73.60067

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