For uniformly elliptic operators with DMO-type coefficients, the paper establishes a rectifiability criterion for the gradient of the single layer potential, a suppressed T b theorem for Dini kernels, and applications to one- and two-phase free boundary problems for elliptic measure.
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Layer potentials for elliptic operators with DMO-type coefficients: big pieces $Tb$ theorem, quantitative rectifiability, and free boundary problems
For uniformly elliptic operators with DMO-type coefficients, the paper establishes a rectifiability criterion for the gradient of the single layer potential, a suppressed T b theorem for Dini kernels, and applications to one- and two-phase free boundary problems for elliptic measure.