Year: 2024
Type: article
Abstract: We consider capillarity functionals which measure the perimeter of sets contained in a Euclidean half-space assigning a constant weight $$\lambda \in (-1,1)$$ λ ∈ ( - 1 , 1 ) to the portion of the boundary that touches the boundary of the half-space. Depending on $$\lambda $$ λ , sets that minimize this capillarity perimeter among those with fixed volume are known to be suitable truncated balls lying on the boundary of the half-space. We first give a new proof based on an ABP-type technique of the sharp isoperimetric inequality for this class of capillarity problems. Next we prove two quantitative versions of the inequality: a first sharp inequality estimates the Fraenkel asymmetry of a competitor with respect to the optimal bubbles in terms of the energy deficit; a second inequality estimates a notion of asymmetry for the part of the boundary of a competitor that touches the boundary of the half-space in terms of the energy deficit. After a symmetrization procedure, the quantitative inequalities follow from a novel combination of a quantitative ABP method with a selection-type argument.
Authors: Giulio Pascale, Marco Pozzetta
Institution: University of Naples Federico II
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4403001249