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Conjecture on the sharp Sobolev regularity of planar infinity-harmonic functions
Let $u$ be a planar $\infty$ -harmonic function. The preceding results establish Sobolev regularity for powers of $|Du|$ and measure bounds for the distributional determinant, motiv…
Conjectureopeninfinity-harmonic-functions planar-analysis sobolev-regularityarXiv posted 2 days ago
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The capacity-deficit asymptotic conjecture for planar shrinking condensers
Let $\Delta$ be the unit disc in the complex plane, let $\mathbb T=\partial\Delta$ , and let $E\subseteq\mathbb T$ be closed. For $0<r<1$ , write…
Conjectureopencapacity planar-analysis potential-theoryarXiv posted 2 days ago

Conjecture on the sharp Sobolev regularity of planar infinity-harmonic functions