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On the regularity of elliptic differential equations using symmetry techniques and suitable discrete spaces. (English) Zbl 0885.35019

Summary: We present an elementary and short proof for regularity of second order elliptic differential equations with homogeneous Dirichlet boundary conditions. The proof uses a discrete function space with piecewise multilinear functions and symmetry techniques on the unit cube.

MSC:

35B65 Smoothness and regularity of solutions to PDEs
35J25 Boundary value problems for second-order elliptic equations
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