 
Summary: Schauder estimates for a class of second order elliptic
operators on a cube
Sandra Cerrai
Dip. Matematica per le Decisioni
Universit`a di Firenze
Via C. Lombroso 6/17
I50134 Firenze, Italy.
Philippe ClŽement
Dept. of Applied Mathematical Analysis
Technische Universiteit Delft
Mekelweg 4
2628 CD Delft, The Netherlands.
Abstract
We consider a class of second order elliptic operators on a ddimensional cube Sd.
We prove that if the coefficients are of class C k+
(Sd), with k = 0, 1 and (0, 1),
then the corresponding elliptic problem admits a unique solution u belonging to
C k+2+
(Sd) and satisfying non standard boundary conditions involving only second
order derivatives.
