Stability of the $L_p$ torsional measure for $p\gt1$ and $p \neq n+2$

This paper studies the stability of the L p torsional measure in dimension n 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 = n + 2. In terms of L c -distance, the result has been split into two cases: p (1, n), and n < p = n + 2.