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A famous theorem of Bers and Finn states that isolated singularities of solutions to the non-parametric minimal surface equation are removable. We show that this result remains valid, if the area functional is replaced by a general functional of linear growth depending on the modulus of the gradient.

calculus of variations and partial differential equations

An extension of a theorem of Bers and Finn on the removability of isolated singularities to the Euler–Lagrange equations related to general linear growth problems