An Example of Fractal Singular Homogenization

Abstract

Abstract We construct a sequence of quadratic weighted energy forms in an open domain of the plane, that 𝑀-converges to an energy form with a singular fractal term. The weights belong to the Muckenoupt class 𝐴 2 and have pointwise singularities. The result implies the spectral convergence of a sequence of second-order weighted elliptic operators in divergence form in the plane to a singular elliptic operator with a second order fractal term.