Integrability for solutions to quasilinear elliptic systems

Francesco Leonetti; Pier Vincenzo Petricca

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 3, page 481-487
  • ISSN: 0010-2628

Abstract

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In this paper we prove an estimate for the measure of superlevel sets of weak solutions to quasilinear elliptic systems in divergence form. In some special cases, such an estimate allows us to improve on the integrability of the solution.

How to cite

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Leonetti, Francesco, and Petricca, Pier Vincenzo. "Integrability for solutions to quasilinear elliptic systems." Commentationes Mathematicae Universitatis Carolinae 51.3 (2010): 481-487. <http://eudml.org/doc/38144>.

@article{Leonetti2010,
abstract = {In this paper we prove an estimate for the measure of superlevel sets of weak solutions to quasilinear elliptic systems in divergence form. In some special cases, such an estimate allows us to improve on the integrability of the solution.},
author = {Leonetti, Francesco, Petricca, Pier Vincenzo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {level set; integrability; solution; quasilinear; elliptic; system; quasilinear elliptic system; weak solution; structural condition; higher integrability},
language = {eng},
number = {3},
pages = {481-487},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Integrability for solutions to quasilinear elliptic systems},
url = {http://eudml.org/doc/38144},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Leonetti, Francesco
AU - Petricca, Pier Vincenzo
TI - Integrability for solutions to quasilinear elliptic systems
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 3
SP - 481
EP - 487
AB - In this paper we prove an estimate for the measure of superlevel sets of weak solutions to quasilinear elliptic systems in divergence form. In some special cases, such an estimate allows us to improve on the integrability of the solution.
LA - eng
KW - level set; integrability; solution; quasilinear; elliptic; system; quasilinear elliptic system; weak solution; structural condition; higher integrability
UR - http://eudml.org/doc/38144
ER -

References

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  5. Leonetti F., Petricca P.V., Regularity for solutions to some nonlinear elliptic systems, Complex Var. Elliptic Equ.(to appear). MR2852081
  6. Mandras F., Principio di massimo per una classe di sistemi ellittici degeneri quasi lineari, Rend. Sem. Fac. Sci. Univ. Cagliari 46 (1976), 81–88. MR0445115
  7. Nečas J., Stará J., Principio di massimo per i sistemi ellittici quasi-lineari non diagonali, Boll. Un. Mat. Ital. 6 (1972), 1–10. MR0315281
  8. Šverák V., Yan X., 10.1073/pnas.222494699, Proc. Natl. Acad. Sci. USA 99 (2002), 15269–15276. MR1946762DOI10.1073/pnas.222494699

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