Quasiharmonic fields and Beltrami operators

Claudia Capone

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 2, page 363-377
  • ISSN: 0010-2628

Abstract

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A quasiharmonic field is a pair ℱ = [ B , E ] of vector fields satisfying div B = 0 , curl E = 0 , and coupled by a distorsion inequality. For a given ℱ , 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.

How to cite

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Capone, Claudia. "Quasiharmonic fields and Beltrami operators." Commentationes Mathematicae Universitatis Carolinae 43.2 (2002): 363-377. <http://eudml.org/doc/248989>.

@article{Capone2002,
abstract = {A quasiharmonic field is a pair $\mathcal \{F\} = [B,E]$ of vector fields satisfying $\operatorname\{div\} B=0$, $\operatorname\{curl\} E=0$, and coupled by a distorsion inequality. For a given $\mathcal \{F\}$, we construct a matrix field $\mathcal \{A\}=\mathcal \{A\}[B,E]$ such that $\{\mathcal \{A\}\} E=B$. 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 $\mathcal \{A\}[B,E]$ and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.},
author = {Capone, Claudia},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quasiharmonic fields; Beltrami operator; elliptic partial differential equations; G-convergence; quasiharmonic field; Beltrami operator; elliptic partial differential equation; G-convergence},
language = {eng},
number = {2},
pages = {363-377},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Quasiharmonic fields and Beltrami operators},
url = {http://eudml.org/doc/248989},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Capone, Claudia
TI - Quasiharmonic fields and Beltrami operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 2
SP - 363
EP - 377
AB - A quasiharmonic field is a pair $\mathcal {F} = [B,E]$ of vector fields satisfying $\operatorname{div} B=0$, $\operatorname{curl} E=0$, and coupled by a distorsion inequality. For a given $\mathcal {F}$, we construct a matrix field $\mathcal {A}=\mathcal {A}[B,E]$ such that ${\mathcal {A}} E=B$. 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 $\mathcal {A}[B,E]$ and find their applications to the study of regularity of solutions to elliptic PDEs, and to some questions of G-convergence.
LA - eng
KW - quasiharmonic fields; Beltrami operator; elliptic partial differential equations; G-convergence; quasiharmonic field; Beltrami operator; elliptic partial differential equation; G-convergence
UR - http://eudml.org/doc/248989
ER -

References

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