Symmetry for exterior elliptic problems and two conjectures in potential theory

Boyan Sirakov

Annales de l'I.H.P. Analyse non linéaire (2001)

  • Volume: 18, Issue: 2, page 135-156
  • ISSN: 0294-1449

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Sirakov, Boyan. "Symmetry for exterior elliptic problems and two conjectures in potential theory." Annales de l'I.H.P. Analyse non linéaire 18.2 (2001): 135-156. <http://eudml.org/doc/78515>.

@article{Sirakov2001,
author = {Sirakov, Boyan},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {method of moving planes; topological methods; exterior domains},
language = {eng},
number = {2},
pages = {135-156},
publisher = {Elsevier},
title = {Symmetry for exterior elliptic problems and two conjectures in potential theory},
url = {http://eudml.org/doc/78515},
volume = {18},
year = {2001},
}

TY - JOUR
AU - Sirakov, Boyan
TI - Symmetry for exterior elliptic problems and two conjectures in potential theory
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 2
SP - 135
EP - 156
LA - eng
KW - method of moving planes; topological methods; exterior domains
UR - http://eudml.org/doc/78515
ER -

References

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  2. [2] Amick C.J, Fraenkel L.E, Uniqueness of Hill's spherical vortex, Arch. Rat. Mech. Anal.92 (1986) 91-119. Zbl0609.76018MR816615
  3. [3] Aftalion A, Busca J, Radial symmetry for overdetermined elliptic problems in exterior domains, Arch. Rat. Mech. Anal.143 (1998) 195-206. Zbl0911.35008MR1650014
  4. [4] Berestycki H, Nirenberg L, On the method of moving planes and the sliding method, Bull. Soc. Brazil Mat. Nova Ser.22 (1991) 1-37. Zbl0784.35025MR1159383
  5. [5] Castro A, Shivaji R, Non-negative solutions to a semilinear Dirichlet problem in a ball are positive and radially symmetric, Comm. Partial Differential Equations14 (8&9) (1989) 1091-1100. Zbl0688.35025MR1017065
  6. [6] Gidas B, Ni W.-M, Nirenberg L, Symmetry and related properties via the maximum principle, Comm. Math. Phys.6 (1981) 883-901. Zbl0425.35020MR544879
  7. [7] Gilbarg D, Trudinger N, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. Zbl0562.35001MR737190
  8. [8] Li C, Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains, Comm. Partial Differential Equations16 (1991) 585-615. Zbl0741.35014MR1113099
  9. [9] Pucci P, Serrin J, Zou H, A strong maximum principle and a compact support principle for singular elliptic inequalities, J. Math. Pures Appl.78 (4) (1999) 769-789. Zbl0952.35045MR1715341
  10. [10] Reichel W., Radial symmetry by moving planes for semilinear elliptic BVP's on annuli and other non-convex domains, in: Bandle C. et al. (Eds.), Progress in PDE's: Elliptic and Parabolic Problems, Pitman Res. Notes, Vol. 325, pp. 164–182. Zbl0839.35047
  11. [11] Reichel W, Radial symmetry for elliptic boundary-value problems on exterior domains, Arch. Rat. Mech. Anal.137 (1997) 381-394. Zbl0891.35006MR1463801
  12. [12] Reichel W, Radial symmetry for an electrostatic, a capillarity and some fully nonlinear overdetermined problems on exterior domains, Z. Anal. Anwendungen15 (1996) 619-635. Zbl0857.35010MR1406079
  13. [13] Serrin J, A symmetry theorem in potential theory, Arch. Rat. Mech. Anal.43 (1971) 304-318. Zbl0222.31007MR333220
  14. [14] Serrin J, Zou H, Symmetry of ground states of quasilinear elliptic equations, Arch. Rat. Mech. Anal.148 (4) (1999) 265-290. Zbl0940.35079MR1716665
  15. [15] Willms N.B, Gladwell G, Siegel D, Symmetry theorems for some overdetermined boundary-value problems on ring domains, Z. Angew. Math. Phys.45 (1994) 556-579. Zbl0807.35099MR1289661
  16. [16] Vazquez J.-L, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. and Optimisation12 (1984) 191-202. Zbl0561.35003MR768629

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