0000000000347073

AUTHOR

Carlo Sbordone

showing 2 related works from this author

MAPPINGS OF FINITE DISTORTION: $L^n \log^{\alpha} L$ -INTEGRABILITY

2003

Recently, systematic studies of mappings of finite distortion have emerged as a key area in geometric function theory. The connection with deformations of elastic bodies and regularity of energy minimizers in the theory of nonlinear elasticity is perhaps a primary motivation for such studies, but there are many other applications as well, particularly in holomorphic dynamics and also in the study of first order degenerate elliptic systems, for instance the Beltrami systems we consider here.

Distortion (mathematics)Pure mathematicsGeometric function theoryElliptic systemsGeneral MathematicsDegenerate energy levelsHolomorphic functionTopologyFirst orderNonlinear elasticityConnection (mathematics)MathematicsJournal of the London Mathematical Society
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Anisotropic Sobolev homeomorphisms

2011

Let › ‰ R 2 be a domain. Suppose that f 2 W 1;1 loc (›;R 2 ) is a homeomorphism. Then the components x(w), y(w) of the inverse f i1 = (x;y): › 0 ! › have total variations given by jryj(› 0 ) = › fl fl @f fl fl dz; jrxj(› 0 ) = › fl fl @f @y fl fl dz:

Sobolev spacePure mathematicsGeneral MathematicsA domainInverseSobolev homeomorphismsAnisotropyHomeomorphismMathematicsAnnales Academiae Scientiarum Fennicae Mathematica
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