For 𝑠 \in (0, 1) small, we show that the only cones in R2 stationary for the 𝑠-perimeter and stable in R2 ⧵ {0} are half-planes. This is in direct contrast with the case of the classical perimeter or the regime 𝑠 close to 1, where nontrivial cones as {𝑥𝑦 > 0} \subset R2 are stable for inner variations.
Stable 𝑠-minimal cones in R2 are flat for 𝑠 ∼ 0
Caselli, Michele
2025
Abstract
For 𝑠 \in (0, 1) small, we show that the only cones in R2 stationary for the 𝑠-perimeter and stable in R2 ⧵ {0} are half-planes. This is in direct contrast with the case of the classical perimeter or the regime 𝑠 close to 1, where nontrivial cones as {𝑥𝑦 > 0} \subset R2 are stable for inner variations.File in questo prodotto:
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Stability_of_s_min_cones_dim_2__Nonlinear_Analysis_-3.pdf
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