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Isomorphisms of Royden Type Algebras Over 𝕊 1

Teresa RadiceEero SaksmanGabriella Zecca — 2009

Bollettino dell'Unione Matematica Italiana

Let 𝕊 1 and 𝔻 be the unit circle and the unit disc in the plane and let us denote by 𝒜 ( 𝕊 1 ) the algebra of the complex-valued continuous functions on 𝕊 1 which are traces of functions in the Sobolev class W 1 , 2 ( 𝔻 ) . On 𝒜 ( 𝕊 1 ) we define the following norm u = u L ( 𝕊 1 ) + ( 𝔻 | u ~ | 2 ) 1 / 2 where is the harmonic extension of u to 𝔻 . We prove that every isomorphism of the functional algebra 𝒜 ( 𝕊 1 ) is a quasitsymmetric change of variables on 𝕊 1 .

Divergence forms of the infinity-Laplacian.

Luigi D'OnofrioFlavia GiannettiTadeusz IwaniecJuan ManfrediTeresa Radice — 2006

Publicacions Matemàtiques

The central theme running through our investigation is the infinity-Laplacian operator in the plane. Upon multiplication by a suitable function we express it in divergence form, this allows us to speak of weak infinity-harmonic function in W1,2. To every infinity-harmonic function u we associate its conjugate function v. We focus our attention to the first order Beltrami type equation for h= u + iv

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