Partial Regularity for Stationary Solutions to Liouville-Type Equation in dimension 3
classification
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keywords
dimensionequationstationarybelongsdeltahausdorffliouvilleliouville-type
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In dimension $n=3$, we prove that the singular set of any stationary solution to the Liouville equation $-\Delta u=e^u$, which belongs to $W^{1,2}$, has Hausdorff dimension at most 1.
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