Harmonic homeomorphisms of the closed disc to itself need be in 𝑊^{{}1,𝑝}, 𝑝<2, but not 𝑊^{{}1,2}

Verchota, Gregory

doi:10.1090/S0002-9939-06-08506-6

Harmonic homeomorphisms of the closed disc to itself need be in $W^\{1,p\}$, $p<2$, but not $W^\{1,2\}$
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Proc. Amer. Math. Soc. 135 (2007), 891-894 Request permission

Abstract:

Harmonic maps $u$ from the closed disc onto bounded convex sets of the plane obey $u\in W^{1,p}, p<2$.

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