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Abstract
Let ƒ : B → ℂ denote a Sobolev function of class defined on the unit disc. We show that the distance of ƒ to the class of all holomorphic functions measured in the norm of the space
is bounded by the Lp-norm of theWirtinger derivative
. As a consequence we obtain a Korn type inequality for vector fields
.
Received: 2009-10-05
Revised: 2010-05-24
Accepted: 2010-06-07
Published Online: 2011-05-04
Published in Print: 2011-June
© de Gruyter 2011