Mathematical analysis reveals sharp Hausdorff dimension estimates for boundary blow-up sets of semilinear elliptic equations, highlighting constraints on positive solution growth.
We estimate the Hausdorff dimension of a subset of the unit sphere where a positive solution of a semilinear elliptic equation with source term of negative exponent in the unit ball grows faster than a prescribed order. Also, the sharpness of our estimate is shown by proving the existence of a positive solution growing faster than a prescribed order on a given subset of the unit sphere.
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Kentaro Hirata (2026) studied this question.
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