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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 𝐴2 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.
Key words and phrases:: Fractal singular homogenization; weighted elliptic operators
Received: 2006-11-09
Published Online: 2010-03-10
Published in Print: 2007-March
© Heldermann Verlag
