Boundary derivatives of p-harmonic functions explode at rate C_Ω/(p-1) or decay exponentially as p→1, with the regime determined nonlocally by the domain; a cylinder yields the intermediate rate C_d/√(p-1).
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Explosion versus decay for boundary derivatives of $p$-harmonic functions as $p$ tends to 1: nonlocality
Boundary derivatives of p-harmonic functions explode at rate C_Ω/(p-1) or decay exponentially as p→1, with the regime determined nonlocally by the domain; a cylinder yields the intermediate rate C_d/√(p-1).