We consider a class of second order elliptic operators on a d-dimensional cube Sd. We prove that if the coefficients are of class Ck+δ(Sd), with k=0,1 and δ∈(0,1), then the corresponding elliptic problem admits a unique solution u belonging to Ck+2+δ(Sd) and satisfying non-standard boundary conditions involving only second order derivatives.
Schauder estimates for a class of second order elliptic operators on a cube / S. CERRAI; P. CLEMENT. - In: BULLETIN DES SCIENCES MATHEMATIQUES. - ISSN 0007-4497. - STAMPA. - 217:(2003), pp. 669-688. [10.1016/S0007-4497(03)00058-7]
Schauder estimates for a class of second order elliptic operators on a cube
CERRAI, SANDRA;
2003
Abstract
We consider a class of second order elliptic operators on a d-dimensional cube Sd. We prove that if the coefficients are of class Ck+δ(Sd), with k=0,1 and δ∈(0,1), then the corresponding elliptic problem admits a unique solution u belonging to Ck+2+δ(Sd) and satisfying non-standard boundary conditions involving only second order derivatives.
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