A dimension-free hermite-hadamard inequality via gradient estimates for the torsion function
Let Ω ⊂ Rn be a convex domain, and let f : Ω → R be a subharmonic function, Δf ≥ 0, which satisfies f ≥ 0 on the boundary ∂Ω. Then (Formula Presented) Our proof is based on a new gradient estimate for the torsion function, Δu = -1 with Dirichlet boundary conditions, which is of independent interest.
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