Constructs bounded non-spherical finite-perimeter domains satisfying distributional Bernoulli laws with unbounded reduced-boundary density, yielding counterexamples to weak Serrin problems in all dimensions, plus 2D rigidity under Smirnov class.
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Serrin's overdetermined theorem and weak Bernoulli laws without Alt--Caffarelli regularity
Constructs bounded non-spherical finite-perimeter domains satisfying distributional Bernoulli laws with unbounded reduced-boundary density, yielding counterexamples to weak Serrin problems in all dimensions, plus 2D rigidity under Smirnov class.