Inheritance of symmetry for positive solutions of semilinear elliptic boundary value problems

Bernd Kawohl; Guido Sweers

Annales de l'I.H.P. Analyse non linéaire (2002)

  • Volume: 19, Issue: 5, page 705-714
  • ISSN: 0294-1449

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Kawohl, Bernd, and Sweers, Guido. "Inheritance of symmetry for positive solutions of semilinear elliptic boundary value problems." Annales de l'I.H.P. Analyse non linéaire 19.5 (2002): 705-714. <http://eudml.org/doc/78559>.

@article{Kawohl2002,
author = {Kawohl, Bernd, Sweers, Guido},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Steiner symmetry; non-convex symmetrical domains; sliding method; maximum principle},
language = {eng},
number = {5},
pages = {705-714},
publisher = {Elsevier},
title = {Inheritance of symmetry for positive solutions of semilinear elliptic boundary value problems},
url = {http://eudml.org/doc/78559},
volume = {19},
year = {2002},
}

TY - JOUR
AU - Kawohl, Bernd
AU - Sweers, Guido
TI - Inheritance of symmetry for positive solutions of semilinear elliptic boundary value problems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2002
PB - Elsevier
VL - 19
IS - 5
SP - 705
EP - 714
LA - eng
KW - Steiner symmetry; non-convex symmetrical domains; sliding method; maximum principle
UR - http://eudml.org/doc/78559
ER -

References

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  1. [1] Altmann S.L., Herzig P., Point-Group Theory Tables, Clarendon Press, Oxford, 1994. 
  2. [2] Berestycki H., Nirenberg L., Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations, J. Geom. Phys.5 (1988) 237-275. Zbl0698.35031MR1029429
  3. [3] Berestycki H., Nirenberg L., On the method of moving planes and the sliding method, Bol. Soc. Brasil. Mat. (N.S.)22 (1991) 1-37. Zbl0784.35025MR1159383
  4. [4] Coffman C.V., A nonlinear boundary value problem with many positive solutions, J. Differential Equations54 (1984) 429-437. Zbl0569.35033MR760381
  5. [5] Coxeter H.S.M., Regular Polytopes, Dover Publications, New York, 1973. Zbl0118.35902MR370327
  6. [6] Dancer E.N., The effect of the domain shape on the number of positive solutions of certain nonlinear equations, J. Differential Equations74 (1988) 120-156. Zbl0662.34025MR949628
  7. [7] Dancer E.N., Sweers G., On the existence of a maximal weak solution for a semilinear elliptic equation, Differential Integral Equations2 (1989) 533-540. Zbl0732.35027MR996759
  8. [8] Fraenkel L.E., An Introduction to Maximum Principles and Symmetry in Elliptic Problems, Cambridge Tracts in Mathematics, 128, Cambridge University Press, Cambridge, 2000. Zbl0947.35002MR1751289
  9. [9] Gidas B., Ni W.M., Nirenberg L., Symmetry and related properties via the maximum principle, Comm. Math. Phys.68 (1979) 209-243. Zbl0425.35020MR544879
  10. [10] Kawohl B., A geometric property of level sets of solutions to semilinear elliptic Dirichlet problems, Applicable Anal.16 (1983) 229-233. Zbl0507.35035MR712734
  11. [11] Kawohl B., Symmetry results for functions yielding best constants in Sobolev-type inequalities, Discrete Continuous Dynam. Systems6 (2000) 683-690. Zbl1157.35342MR1757396
  12. [12] McNabb A., A. Strong comparison theorems for elliptic equations of second order, J. Math. Mech.10 (1961) 431-440. Zbl0106.29903MR142881
  13. [13] McWeeny R., Symmetry, an Introduction to Group Theory and Its Applications, Pergamon Press, Oxford, 1963. Zbl0111.36002MR224687
  14. [14] Sweers G., Semilinear elliptic problems on domains with corners, Comm. Partial Differential Equations14 (1989) 1229-1247. Zbl0702.35097MR1017071
  15. [15] Sweers G., Lecture notes on maximum principles, December 2000, http://aw.twi.tudelft.nl/~sweers/maxpr/maxprinc.pdf. 

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