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Keywords:
quasiharmonic fields; Beltrami operator; elliptic partial differential equations; G-convergence
quasiharmonic fields; Beltrami operator; elliptic partial differential equations; G-convergence
Summary:
A quasiharmonic field is a pair $\Cal{F} = [B,E]$ of vector fields satisfying $\operatorname{div} B=0$, $\operatorname{curl} E=0$, 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. 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.
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