On a Regularity of Biharmonic Approximations to a Nonlinear Degenerate Elliptic PDE

Abstract

Under appropriate assumption on the coefficients, we prove that a

sequence of biharmonic regularization to a nonlinear degenerate

elliptic equation with possibly rough coefficients preserves

certain regularity as the approximation parameter tends to zero. In

order to obtain the result, we introduce a generalization of the

Chebyshev inequality. We also present numerical example.