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Stability of the
$L_p$ torsional measure for 
$p>$ 1 and 
$p\neq n\ +$ 2
- Part of
-
- Journal:
- Canadian Journal of Mathematics , First View
- Published online by Cambridge University Press:
- 18 February 2026, pp. 1-27
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- Article
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This article studies the stability of the
$L_p$ torsional measure in dimension 
$n \geq 3$. We show that the ball is the unique domain for the solution to the related overdetermined boundary value problem. Two concepts of relative asymmetry distance and 
$L^c$-distance have been used to estimate the stability of the 
$L_p$ torsional measure, based on different stability results of the 
$L_p$-width functionals. The result has been uniformly given via relative asymmetry distance for all 
$1<p \neq n+2$. In terms of 
$L^c$-distance, the result has been split into two cases: 
$p\in (1,n)$, and 
$n< p\neq n+2$.
