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

Andrej Novak, Jela Šušić

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.