@article{AIHPC_2008__25_2_281_0, author = {Gazzini, Marita and Serra, Enrico}, title = {The {Neumann} problem for the {H\'enon} equation, trace inequalities and {Steklov} eigenvalues}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {281--302}, publisher = {Elsevier}, volume = {25}, number = {2}, year = {2008}, doi = {10.1016/j.anihpc.2006.09.003}, mrnumber = {2396523}, zbl = {1138.35024}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.09.003/} }
TY - JOUR AU - Gazzini, Marita AU - Serra, Enrico TI - The Neumann problem for the Hénon equation, trace inequalities and Steklov eigenvalues JO - Annales de l'I.H.P. Analyse non linéaire PY - 2008 SP - 281 EP - 302 VL - 25 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2006.09.003/ DO - 10.1016/j.anihpc.2006.09.003 LA - en ID - AIHPC_2008__25_2_281_0 ER -
%0 Journal Article %A Gazzini, Marita %A Serra, Enrico %T The Neumann problem for the Hénon equation, trace inequalities and Steklov eigenvalues %J Annales de l'I.H.P. Analyse non linéaire %D 2008 %P 281-302 %V 25 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2006.09.003/ %R 10.1016/j.anihpc.2006.09.003 %G en %F AIHPC_2008__25_2_281_0
Gazzini, Marita; Serra, Enrico. The Neumann problem for the Hénon equation, trace inequalities and Steklov eigenvalues. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 2, pp. 281-302. doi : 10.1016/j.anihpc.2006.09.003. http://www.numdam.org/articles/10.1016/j.anihpc.2006.09.003/
[1] Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, vol. 55, 1964. | MR | Zbl
, ,[2] Isoperimetric Inequalities and Applications, Monographs and Studies in Mathematics, vol. 7, Pitman, Boston, MA, 1980. | MR | Zbl
,[3] Multiplicity results for the supercritical Hénon equation, Adv. Nonlinear Stud. 4 (4) (2004) 453-467. | MR | Zbl
, ,[4] J. Byeon, Z.-Q. Wang, On the Hénon equation: asymptotic profile of ground states, preprint, 2002.
[5] On the Hénon equation: asymptotic profile of ground states, II, J. Differential Equations 216 (2005) 78-108. | MR | Zbl
, ,[6] The asymptotic behaviour of the ground state solutions for Hénon equation, J. Math. Anal. Appl. 278 (1) (2003) 1-17. | MR | Zbl
, ,[7] Asymptotic behavior of best constants and extremals for trace embeddings in expanding domains, Comm. Partial Differential Equations 26 (11) (2001) 2189-2210. | MR | Zbl
, ,[8] Sharp constant in a Sobolev trace inequality, Indiana Univ. Math. J. 37 (3) (1988) 687-698. | MR | Zbl
,[9] Symmetry properties for the extremals of the Sobolev trace embedding, Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (6) (2004) 795-805. | Numdam | MR
, , ,[10] On the existence of extremals of the Sobolev trace embedding theorem with critical exponent, Bull. London Math. Soc. 37 (1) (2005) 119-125. | MR | Zbl
, ,[11] Symmetries and related properties via the maximum principle, Comm. Math. Phys. 68 (1979) 209-243. | MR | Zbl
, , ,[12] Numerical experiments on the stability of spherical stellar systems, Astronomy and Astrophysics 24 (1973) 229-238.
,[13] Symmetry and symmetry breaking for minimizers in the trace inequality, Comm. Contemp. Math. 7 (6) (2005) 727-746. | MR
, ,[14] A nonlinear Dirichlet problem on the unit ball and its applications, Indiana Univ. Math. J. 31 (6) (1982) 801-807. | MR | Zbl
,[15] A. Pistoia, E. Serra, Multi-peak solutions for the Hénon equation with slightly subcritical growth, Math. Zeit., submitted for publication. | Zbl
[16] Non radial positive solutions for the Hénon equation with critical growth, Calc. Var. Partial Differential Equations 23 (3) (2005) 301-326. | MR
,[17] Symmetry breaking results for problems with exponential growth in the unit disk, Comm. Contemp. Math. 8 (6) (2006) 823-839. | MR
, ,[18] Non radial ground states for the Hénon equation, Comm. Contemp. Math. 4 (3) (2002) 467-480. | MR | Zbl
, , ,[19] Partial symmetry and asymptotic behavior for some elliptic variational problems, Calc. Var. Partial Differential Equations 18 (2003) 57-75. | MR
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