BMO and Lipschitz approximation by solutions of elliptic equations

Joan Mateu; Yuri Netrusov; Joan Orobitg; Joan Verdera

Annales de l'institut Fourier (1996)

  • Volume: 46, Issue: 4, page 1057-1081
  • ISSN: 0373-0956

Abstract

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We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known: we find a sufficient condition for the approximation reducing matters to a weak * spectral synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditions are sharp.

How to cite

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Mateu, Joan, et al. "BMO and Lipschitz approximation by solutions of elliptic equations." Annales de l'institut Fourier 46.4 (1996): 1057-1081. <http://eudml.org/doc/75199>.

@article{Mateu1996,
abstract = {We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known: we find a sufficient condition for the approximation reducing matters to a weak $*$ spectral synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditions are sharp.},
author = {Mateu, Joan, Netrusov, Yuri, Orobitg, Joan, Verdera, Joan},
journal = {Annales de l'institut Fourier},
keywords = {spectral synthesis; elliptic approximation; Lizorkin-Triebel spaces},
language = {eng},
number = {4},
pages = {1057-1081},
publisher = {Association des Annales de l'Institut Fourier},
title = {BMO and Lipschitz approximation by solutions of elliptic equations},
url = {http://eudml.org/doc/75199},
volume = {46},
year = {1996},
}

TY - JOUR
AU - Mateu, Joan
AU - Netrusov, Yuri
AU - Orobitg, Joan
AU - Verdera, Joan
TI - BMO and Lipschitz approximation by solutions of elliptic equations
JO - Annales de l'institut Fourier
PY - 1996
PB - Association des Annales de l'Institut Fourier
VL - 46
IS - 4
SP - 1057
EP - 1081
AB - We consider the problem of qualitative approximation by solutions of a constant coefficients homogeneous elliptic equation in the Lipschitz and BMO norms. Our method of proof is well-known: we find a sufficient condition for the approximation reducing matters to a weak $*$ spectral synthesis problem in an appropriate Lizorkin-Triebel space. A couple of examples, evolving from one due to Hedberg, show that our conditions are sharp.
LA - eng
KW - spectral synthesis; elliptic approximation; Lizorkin-Triebel spaces
UR - http://eudml.org/doc/75199
ER -

References

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