Optimal quantitative stability for a Serrin-type problem in convex cones

We consider a Serrin's type problem in convex cones in the Euclidean space and motivated by recent rigidity results we study the quantitative stability issue for this problem. In particular, we prove both sharp Lipschitz estimates for an L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>2$$\end{document}-pseudodistance and estimates in terms of the Hausdorff distance.