  In this paper, we introduce a notion of capillary Schwarz symmetrization in
the half-space. It can be viewed as the counterpart of the classical Schwarz
symmetrization in the framework of capillary problem in the half-space. A key
ingredient is a special anisotropic gauge, which enables us to transform the
capillary symmetrization to the convex symmetrization introduced in
\cite{AFT97}.
