Elliptic difference equations and interior regularity. (English) Zbl 0159.38204

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[1] Bramble, J. H.: A second order finite difference analogue of the first biharmonic boundary value problem. Numer. Math.9, 236–249 (1966). · Zbl 0154.41105
[2] —-, andB. E. Hubbard: A theorem on error estimation for finite difference analogues of the Dirichlet problem for elliptic equations. Contributions to Differential Equations2, 319–340 (1963).
[3] —-, —- Approximation of derivatives by finite difference methods in elliptic boundary value problems. Contributions to Differential Equations3, 399–410 (1964).
[4] Courant, R., K. Friedrichs u.H. Lewy: Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann.100, 32–74 (1928). · JFM 54.0486.01
[5] Friedrichs, K. O.: On the differentiability of solutions of linear elliptic differential equations. Comm. Pure Appl. Math.6, 299–326 (1953). · Zbl 0051.32703
[6] Sobolev, S. L.: On estimates for certain sums for functions defined on a grid. Izv. Akad. Nauk SSSR, Ser. Mat.4, 5–16 (1940).
[7] Stummel, F.: Elliptische Differenzenoperatoren unter Dirichlet-Randbedingungen. Math. Z.97, 169–211 (1967). · Zbl 0149.07202
[8] Thomée, V.: Elliptic difference operators and Dirichlet’s problem. Contributions to Differential Equations3, 301–324 (1964).
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