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Quasiharmonic fields and Beltrami operators

Claudia Capone (2002)

Commentationes Mathematicae Universitatis Carolinae

A quasiharmonic field is a pair = [ B , E ] of vector fields satisfying div B = 0 , curl E = 0 , and coupled by a distorsion inequality. For a given , we construct a matrix field 𝒜 = 𝒜 [ B , E ] such that 𝒜 E = B . This remark in particular shows that the theory of quasiharmonic fields is equivalent (at least locally) to that of elliptic PDEs. Here we stress some properties of our operator 𝒜 [ B , E ] and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.

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