On the L^p norm of the torsion unction

2018/02/15 by Berg, Michiel van den, Kappeler, Thomas
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1802.05499

Abstract

Bounds are obtained for the L^p norm of the torsion function v_Ω, i.e. the solution of -Δv=1, v∈ H₀¹(Ω), in terms of the Lebesgue measure of Ω and the principal eigenvalue λ₁(Ω) of the Dirichlet Laplacian acting in L²(Ω). We show that these bounds are sharp for 1≤ p≤ 2.

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