L p -Estimates for linear elliptic systems with discontinuous coefficients

Filippo Chiarenza; Michelangelo Franciosi; Michele Frasca

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 1, page 27-32
  • ISSN: 1120-6330

Abstract

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In this Note we give L p estimates 1 < p < + ∞ for the highest order derivatives of an elliptic system in non-divergence form with coefficients in VMO.

How to cite

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Chiarenza, Filippo, Franciosi, Michelangelo, and Frasca, Michele. "\( L^{p} \)-Estimates for linear elliptic systems with discontinuous coefficients." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.1 (1994): 27-32. <http://eudml.org/doc/244091>.

@article{Chiarenza1994,
abstract = {In this Note we give \( L^\{p\} \) estimates \( ( 1 < p < + \infty ) \) for the highest order derivatives of an elliptic system in non-divergence form with coefficients in VMO.},
author = {Chiarenza, Filippo, Franciosi, Michelangelo, Frasca, Michele},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Elliptics systems; $ L^\{p\} $ L p -Estimates; VMO; estimates for the highest order derivatives; elliptic system in non-divergence form; coefficients in VMO},
language = {eng},
month = {3},
number = {1},
pages = {27-32},
publisher = {Accademia Nazionale dei Lincei},
title = {\( L^\{p\} \)-Estimates for linear elliptic systems with discontinuous coefficients},
url = {http://eudml.org/doc/244091},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Chiarenza, Filippo
AU - Franciosi, Michelangelo
AU - Frasca, Michele
TI - \( L^{p} \)-Estimates for linear elliptic systems with discontinuous coefficients
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/3//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 1
SP - 27
EP - 32
AB - In this Note we give \( L^{p} \) estimates \( ( 1 < p < + \infty ) \) for the highest order derivatives of an elliptic system in non-divergence form with coefficients in VMO.
LA - eng
KW - Elliptics systems; $ L^{p} $ L p -Estimates; VMO; estimates for the highest order derivatives; elliptic system in non-divergence form; coefficients in VMO
UR - http://eudml.org/doc/244091
ER -

References

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  1. AGMON, S. - DOUGLIS, A. - NIRENBERG, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math., vol. 12, 1959, 623-727. Zbl0093.10401MR125307
  2. AGMON, S. - DOUGLIS, A. - NIRENBERG, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Comm. Pure Appl. Math., vol. 17, 1964, 35-72. Zbl0123.28706MR162050
  3. BUREAU, F., Divergent integrals and partial differential equations. Comm. Pure Appl. Math., vol. 8, 1955, 143-202. Zbl0064.09204MR68085
  4. CAFFARELLI, L., Interior a priori estimates for solutions of fully non-linear equations. Annals of Math., vol. 130, 1989, 189-213. Zbl0692.35017MR1005611DOI10.2307/1971480
  5. CAMPANATO, S., Sistemi parabolici del secondo ordine, non variazionali, a coefficienti discontinui. Ann. Univ. Ferrara, vol. 23, 1977, 169-187. Zbl0372.35043MR473529
  6. CHIARENZA, F. - FRASCA, M. - LONGO, P., Interior W 2 , p -estimates for non divergence elliptic equations with discontinuous coefficients. Ricerche di Matem., vol. 40, 1991, 149-168. Zbl0772.35017MR1191890
  7. CHIARENZA, F. - FRASCA, M. - LONGO, P., W 2 , p -solvability of the Dirichlet problem for non divergence elliptic equations with VMO coefficients. Trans. Amer. Math. Soc., vol. 336, 1993, 841-853. Zbl0818.35023MR1088476DOI10.2307/2154379
  8. DOUGLIS, A. - NIRENBERG, L., Interior estimates for elliptic systems of partial differential equations. Comm. Pure Appl. Math., vol. 8, 1955, 503-538. Zbl0066.08002MR75417
  9. JOHN, F., The fundamental solution of linear elliptic differential equations with analytic coefficients. Comm. Pure Appl. Math., vol. 3, 1950, 273-304. Zbl0041.06203MR42030
  10. JOHN, F. - NIRENBERG, L., On functions of bounded mean oscillation. Comm. Pure Appl. Math., vol. 14, 1961, 415-476. Zbl0102.04302MR131498
  11. SARASON, D., Functions of vanishing mean oscillation. Trans. Amer. Math. Soc., vol. 207, 1975, 391-405. Zbl0319.42006MR377518
  12. TORCHINSKY, A., Real-variable methods in harmonic analysis. Academic Press, New York1986. Zbl0621.42001MR869816

Citations in EuDML Documents

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  1. Dian K. Palagachev, Lubomira G. Softova, Characterization of the interior regularity for parabolic systems with discontinuous coefficients
  2. Michelangelo Franciosi, A condition implying boundedness and VMO for a function f
  3. P. Auscher, M. Qafsaoui, Observations on W 1 , p estimates for divergence elliptic equations with VMO coefficients
  4. Giuseppe Di Fazio, Maria Stella Fanciullo, Gradient estimates for elliptic systems in Carnot-Carathéodory spaces
  5. Chiarenza, Filippo, L p -regularity for systems of PDE’s, with coefficients in VMO

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