For bounded corkscrew domains with uniformly n-rectifiable boundary, the normal derivative of the harmonic solution is controlled in total variation by the Hajłasz gradient of the boundary data, and a converse characterizes uniform rectifiability in the plane.
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One-sided Rellich inequalities, Regularity problem and uniform rectifiability
For bounded corkscrew domains with uniformly n-rectifiable boundary, the normal derivative of the harmonic solution is controlled in total variation by the Hajłasz gradient of the boundary data, and a converse characterizes uniform rectifiability in the plane.