Abstract
The authors study an example, suggested by E. De Giorgi, of a second-order uniformly elliptic partial differential operator in divergence form with continuous coefficients on a smooth domain in the plane such that the associated “harmonic measure“ on the boundary is not absolutely continuous with respect to the ordinary surface measure.
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Modica, L., Mortola, S. Construction of a singular elliptic-harmonic measure. Manuscripta Math 33, 81–98 (1980). https://doi.org/10.1007/BF01298340
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DOI: https://doi.org/10.1007/BF01298340