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 $1$.
Partial Regularity for Stationary Solutions to Liouville-Type Equation in dimension 3
DA LIO, FRANCESCA
2008
Abstract
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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