Pierre Del Castillo
Proof of the Parr Formula for the superheating field
(276K, Poscript)

ABSTRACT.  In \cite{BoHe4}, in order to prove the De Gennes Formula \cite{Ge1966}, C. Bolley and B. Helffer have obtained an upper bound for the superheating field $h^{sh}(\ka)$ in a semi-infinite film in the weak-$\kappa$ limit. Precisely, they have proved that 
$\ka \left(h^{sh}(\ka)\right)^2\leq 2^{-\frac{3}{2}}+\mathcal{O}(\ka^{\frac{1}{2}}).$
In this paper, we improve this result and get the upper bound 
$$
\ka \left(h^{sh}(\ka)\right)^2\leq 2^{-\frac{3}{2}}+\frac{15}{32}\ka+\mathcal{O}(\ka^{1+\rho}),\;\;\;\rho>0.
$$
Combining this result with the lower bound for $h^{sh}(\ka)$ obtained in \cite{Ca1}, we deduce the Parr Formula~\cite{parr}.