Geodesic
Quasiharmonic fields and Beltrami operators
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 363-377 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 30C65, 35B40, 35B45, 35D10, 35J20, 35J60, 47B99, 47F05
Keywords: quasiharmonic fields; Beltrami operator; elliptic partial differential equations; G-convergence 
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     author = {Capone, Claudia},
     title = {Quasiharmonic fields and {Beltrami} operators},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {363--377},
     year = {2002},
     volume = {43},
     number = {2},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2002_43_2_a13/}
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Capone, Claudia. Quasiharmonic fields and Beltrami operators. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 2, pp. 363-377. http://geodesic.mathdoc.fr/item/CMUC_2002_43_2_a13/