Claudia Capone
Quasiharmonic fields and Beltrami operators

Comment.Math.Univ.Carolinae 43,2 (2002) 363-377.

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

Keywords: quasiharmonic fields, Beltrami operator, elliptic partial differential equations, G-convergence
AMS Subject Classification: 47B99, 35J20, 35D10, 35B40