We study stability of minimizers for several geometric problems. Applying second variation techniques and some free boundary regularity results we are able to prove sharp quantitative isocapacitary inequality, both in the case of standard capacity and that of p-capacity. With the same approach we deduce that charged liquid droplets minimizing Debye-Hückel-type free energy are spherical in the small charge regime.
Second variation techniques for stability in geometric inequalities / Mukoseeva, Ekaterina. - (2020 Sep 23).
|Titolo:||Second variation techniques for stability in geometric inequalities|
|Data di pubblicazione:||23-set-2020|
|Appare nelle tipologie:||8.1 PhD thesis|