Schauder estimates for a class of second order elliptic operators on a cube |
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| Authors: | Sandra Cerrai Philippe Clément |
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| Institution: | a Dip. Matematica per le Decisioni, Università di Firenze, Via C. Lombroso 6/17, 50134 Firenze, Italy
b Department of Applied Mathematical Analysis, Technische Universiteit Delft, Mekelweg 4, 2628 CD Delft, The Netherlands |
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| 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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| Keywords: | 35B45 35B65 35J25 |
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