On the $L^p$ norm of the torsion unction

arxiv: 1802.05499 · v1 · pith:BL6FJB34new · submitted 2018-02-15 · 🧮 math.AP

On the L^p norm of the torsion unction

Michiel van den Berg , Thomas Kappeler This is my paper

classification 🧮 math.AP

keywords omegaboundsnormtorsionactingdeltadirichleteigenvalue

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Bounds are obtained for the $L^p$ norm of the torsion function $v_{\Omega}$, i.e. the solution of $-\Delta v=1,\, v\in H_0^1(\Omega),$ in terms of the Lebesgue measure of $\Omega$ and the principal eigenvalue $\lambda_1(\Omega)$ of the Dirichlet Laplacian acting in $L^2(\Omega)$. We show that these bounds are sharp for $1\le p\le 2$.

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On the L^p norm of the torsion unction

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