| Abstract: |
| The classical capillarity problem consists of minimizing, among sets satisfying a volume constraint within a given container, a suitably weighted perimeter. The contribution of the interface that touches the boundary of the container is weighted by a fixed constant representing the relative adhesion coefficient between the liquid drop and the solid walls of the container. When the container is a half-space, the isoperimetric sets for this problem are suitably truncated balls lying on the boundary of the half-space.
The aim of this talk is to present some quantitative isoperimetric inequalities for the capillarity problem in a half-space, which estimate different notions of asymmetry of a competitor with respect to the optimal bubble in terms of the corresponding isoperimetric deficit. I will also mention some applications in which nonlocal interactions are taken into account. |
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