Neohookean deformations of annuli, existence, uniqueness and radial symmetry

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

Let X = x ∈ ℝ2; r < {pipe}x{pipe} < R} and Y = {y ∈ ℝ2; r* < {pipe}y{pipe} < R* be annuli in the plane. We consider the class F(X, Y) of all orientation preserving homeomorphisms, in the Sobolev space W1,2(X, Y) which keep the boundary circles in the same order. This means that, and,. We study the Neohookean energy integral, where Φ ∈ C(0, ∞) is positive and strictly convex. We assume in addition that the function, and its derivative extend continuously to [0, ∞), with Ψ(0) = 0. Then we prove: Theorem 1 The minimum of energy within the class F (X, Y) is attained for a radial map h(x) = H({pipe}x{pipe}) x/{pipe}x{pipe}. The minimizer is C-smooth and is unique up to a rotation of the annuli. We believe that not only the result but also some novelties in the computation might gain a particular interest.

Original languageEnglish (US)
Pages (from-to)35-55
Number of pages21
JournalMathematische Annalen
Volume348
Issue number1
DOIs
StatePublished - Sep 1 2010

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Neohookean deformations of annuli, existence, uniqueness and radial symmetry'. Together they form a unique fingerprint.

Cite this