Nous obtenons des résultats pour la question suivante, avec et entiers. QuestionPour quelles fonctions continues existe-t-il une fonction continue telle que chaque solution non-negative de
We obtain results for the following question where and are integers. QuestionFor which continuous functions does there exist a continuous function such that every nonnegative solution of
Mots-clés : Isolated singularity, Polyharmonic, Blow-up, Pointwise bound
@article{AIHPC_2013__30_6_1069_0, author = {Taliaferro, Steven D.}, title = {Pointwise bounds and blow-up for nonlinear polyharmonic inequalities}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1069--1096}, publisher = {Elsevier}, volume = {30}, number = {6}, year = {2013}, doi = {10.1016/j.anihpc.2012.12.011}, mrnumber = {3132417}, zbl = {1286.35278}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2012.12.011/} }
TY - JOUR AU - Taliaferro, Steven D. TI - Pointwise bounds and blow-up for nonlinear polyharmonic inequalities JO - Annales de l'I.H.P. Analyse non linéaire PY - 2013 SP - 1069 EP - 1096 VL - 30 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2012.12.011/ DO - 10.1016/j.anihpc.2012.12.011 LA - en ID - AIHPC_2013__30_6_1069_0 ER -
%0 Journal Article %A Taliaferro, Steven D. %T Pointwise bounds and blow-up for nonlinear polyharmonic inequalities %J Annales de l'I.H.P. Analyse non linéaire %D 2013 %P 1069-1096 %V 30 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2012.12.011/ %R 10.1016/j.anihpc.2012.12.011 %G en %F AIHPC_2013__30_6_1069_0
Taliaferro, Steven D. Pointwise bounds and blow-up for nonlinear polyharmonic inequalities. Annales de l'I.H.P. Analyse non linéaire, Tome 30 (2013) no. 6, pp. 1069-1096. doi : 10.1016/j.anihpc.2012.12.011. http://www.numdam.org/articles/10.1016/j.anihpc.2012.12.011/
[1] Nonexistence of positive supersolutions of elliptic equations via the maximum principle, Comm. Partial Differential Equations 36 (2011), 2011-2047 | MR | Zbl
, ,[2] Representation formulae for solutions to some classes of higher order systems and related Liouville theorems, Milan J. Math. 76 (2008), 27-67 | MR | Zbl
, , ,[3] Isolated singularities of polyharmonic equations, Atti Semin. Mat. Fis. Univ. Modena 46 (1998), 257-294 | MR | Zbl
, , ,[4] Nonlinear biharmonic equations with negative exponents, J. Differential Equations 246 (2009), 216-234 | MR | Zbl
, ,[5] Removability of sets for sub-polyharmonic functions, Hiroshima Math. J. 33 (2003), 31-42 | MR | Zbl
, , ,[6] Isolated singularities of super-polyharmonic functions, Hokkaido Math. J. 33 (2004), 675-695 | MR | Zbl
, ,[7] Polyharmonic Boundary Value Problems, Springer (2010) | MR
, , ,[8] Isolated singularities of polyharmonic inequalities, J. Funct. Anal. 261 (2011), 660-680 | MR | Zbl
, , ,[9] Elliptic Partial Differential Equations of Second Order, Springer (1983) | MR | Zbl
, ,[10] Liouville-type theorems for polyharmonic equations in and in , Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), 339-359 | MR | Zbl
, ,[11] Removable singularity of the polyharmonic equation, Nonlinear Anal. 72 (2010), 624-627 | MR | Zbl
,[12] Radial solutions of singular nonlinear biharmonic equations and applications to conformal geometry, Electron. J. Differential Equations 37 (2003) | EuDML | MR | Zbl
, ,[13] A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems, Math. Z. 261 (2009), 805-827 | MR | Zbl
, ,[14] Existence of solutions to nonlinear, subcritical higher order elliptic Dirichlet problems, J. Differential Equations 248 (2010), 1866-1878 | MR | Zbl
, ,[15] On the growth of superharmonic functions near an isolated singularity II, Comm. Partial Differential Equations 26 (2001), 1003-1026 | MR | Zbl
,[16] Isolated singularities on nonlinear elliptic inequalities, Indiana Univ. Math. J. 50 (2001), 1885-1897 | MR | Zbl
,[17] Classification of solutions of higher order conformally invariant equations, Math. Ann. 313 (1999), 207-228 | MR | Zbl
, ,[18] Uniqueness theorem for the entire positive solutions of biharmonic equations in , Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), 651-670 | MR | Zbl
,Cité par Sources :