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A geometric approach to accretivity

Leonid V. Kovalev (2007)

Studia Mathematica

We establish a connection between generalized accretive operators introduced by F. E. Browder and the theory of quasisymmetric mappings in Banach spaces pioneered by J. Väisälä. The interplay of the two fields allows for geometric proofs of continuity, differentiability, and surjectivity of generalized accretive operators.

An inverse Sobolev lemma.

Pekka Koskela (1994)

Revista Matemática Iberoamericana

We establish an inverse Sobolev lemma for quasiconformal mappings and extend a weaker version of the Sobolev lemma for quasiconformal mappings of the unit ball of Rn to the full range 0 < p < n. As an application we obtain sharp integrability theorems for the derivative of a quasiconformal mapping of the unit ball of Rn in terms of the growth of the mapping.

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