Optimal quantitative stability for a Serrin-type problem in convex cones
Filomena Pacella, Giorgio Poggesi, Alberto Roncoroni
TL;DR
This paper investigates the quantitative stability of a Serrin-type problem within convex cones, providing sharp Lipschitz and Hausdorff distance estimates to measure how solutions deviate from ideal configurations.
Contribution
It introduces new sharp Lipschitz and Hausdorff distance estimates for the stability analysis of a Serrin-type problem in convex cones.
Findings
Established sharp Lipschitz estimates for an $L^2$-pseudodistance.
Derived stability estimates in terms of the Hausdorff distance.
Extended rigidity results to quantitative stability measures.
Abstract
We consider a Serrin-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 pseudodistance and estimates in terms of the Hausdorff distance.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Stability and Controllability of Differential Equations