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· 2025 · arXiv 2510.15098

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Lane-Emden Problems on Convex Domains of $\mathbb S^2$

math.AP · 2026-05-28 · unverdicted · novelty 5.0

For 0 ≤ p < 1, u^{(1-p)/2} is strictly concave and for 1 < p ≤ 3 it is strictly convex for positive solutions of the Lane-Emden problem on convex domains in S², implying convex superlevel sets and unique maximum.

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  • Lane-Emden Problems on Convex Domains of $\mathbb S^2$ math.AP · 2026-05-28 · unverdicted · none · ref 7

    For 0 ≤ p < 1, u^{(1-p)/2} is strictly concave and for 1 < p ≤ 3 it is strictly convex for positive solutions of the Lane-Emden problem on convex domains in S², implying convex superlevel sets and unique maximum.