Monotonicity and symmetry of solutions of p -Laplace equations, 1 < p < 2 , via the moving plane method

Lucio Damascelli; Filomena Pacella

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)

  • Volume: 26, Issue: 4, page 689-707
  • ISSN: 0391-173X

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Damascelli, Lucio, and Pacella, Filomena. "Monotonicity and symmetry of solutions of $p$-Laplace equations, $1 &lt; p &lt; 2$, via the moving plane method." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 26.4 (1998): 689-707. <http://eudml.org/doc/84343>.

@article{Damascelli1998,
author = {Damascelli, Lucio, Pacella, Filomena},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {moving plane method; radially symmetric solutions; strictly radially decreasing solutions},
language = {eng},
number = {4},
pages = {689-707},
publisher = {Scuola normale superiore},
title = {Monotonicity and symmetry of solutions of $p$-Laplace equations, $1 &lt; p &lt; 2$, via the moving plane method},
url = {http://eudml.org/doc/84343},
volume = {26},
year = {1998},
}

TY - JOUR
AU - Damascelli, Lucio
AU - Pacella, Filomena
TI - Monotonicity and symmetry of solutions of $p$-Laplace equations, $1 &lt; p &lt; 2$, via the moving plane method
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 26
IS - 4
SP - 689
EP - 707
LA - eng
KW - moving plane method; radially symmetric solutions; strictly radially decreasing solutions
UR - http://eudml.org/doc/84343
ER -

References

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  3. [Br] F. Brock, Continuous Rearrangement and symmetry of solutions of elliptic problems, Habilitation thesis, Cologne (1997). 
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  5. [Da1] L. Damascelli, Some remarks on the method of moving planes, Differential Integral Equations, 11, 3 (1998), 493-501. Zbl1040.35032MR1745551
  6. [Da2] L. Damascelli, Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results, Ann. Inst. H. Poincaré Anal. Non Linéaire, to appear. Zbl0911.35009MR1632933
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  9. [GKPR] M. Grossi - S. Kesavan - F. Pacella - M. Ramaswami, Symmetry of positive solutions of some nonlinear equations, Topol. Methods Nonlinear Analysis, to appear. Zbl0927.35039MR1677751
  10. [H] H. Hopf, "Lectures on differential geometry in the large", Stanford University, 1956. Zbl0669.53001
  11. [KP] S. Kesavan - F. Pacella, Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequality, Appl. Anal.54 (1994), 27-37. Zbl0833.35040MR1382205
  12. [N] A. Norton, A critical set with nonnull image has a large Hausdorff dimension, Trans. Amer. Math. Soc.296 (1986), 367-376. Zbl0596.26008MR837817
  13. [S] J. Serrin, A symmetry problem in potential theory, Arch. Rational Mech. Anal.43 (1971), 304-318. Zbl0222.31007MR333220
  14. [T] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations, J. Diff. Equations51 (1984), 126-150. Zbl0488.35017MR727034
  15. [V] J.L. Vazquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim. (1984), 191-202. Zbl0561.35003MR768629
  16. [W] H. Whitney, A function not constant on a connected set of critical points, Duke Math. J.1 (1935), 514-517. Zbl0013.05801MR1545896JFM61.1117.01

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