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

DOI10.1090/S0002-9939-06-08506-6zbMath1109.31007MaRDI QIDQ3420064

Gregory C. Verchota

Publication date: 1 February 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceDirichlet integralPoisson extension

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Harmonic, subharmonic, superharmonic functions on other spaces (31C05)

Related Items (12)

Sobolev homeomorphic extensions ⋮ Controlled diffeomorphic extension of homeomorphisms ⋮ Grand Sobolev spaces and their applications in geometric function theory and PDEs ⋮ The Sobolev Jordan-Schönflies problem ⋮ Bi-Sobolev extensions ⋮ Sobolev homeomorphic extensions onto John domains ⋮ An embedding theorem for BV-functions ⋮ Sobolev homeomorphic extensions from two to three dimensions ⋮ Recent studies on Sobolev mappings ⋮ Estimates of gradient and of Jacobian of harmonic mappings defined in the unit disk ⋮ Schoenflies solutions of conformal boundary values may fail to be Sobolev ⋮ Improved regularity of harmonic diffeomorphic extensions on quasihyperbolic domains

Cites Work

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• Partial differential equations. 4th ed
• Partial differential equations in the 20th century
• Extremal mappings of finite distortion

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