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.

Nous obtenons des résultats pour la question suivante, avec m1 et n2 entiers. QuestionPour quelles fonctions continues f:[0,)[0,) existe-t-il une fonction continue ϕ:(0,1)(0,) telle que chaque solution C 2m non-negative u(x) de

0-Δ m uf(u)dansB 2 (0){0} n
satisfasse à
u(x)=Oϕ|x|lorsquex0,
et quelle est la meilleure de ces fonctions φ quand elle existe ?

We obtain results for the following question where m1 and n2 are integers. QuestionFor which continuous functions f:[0,)[0,) does there exist a continuous function ϕ:(0,1)(0,) such that every C 2m nonnegative solution u(x) of

0-Δ m uf(u)inB 2 (0){0} n
satisfies
u(x)=Oϕ|x|asx0
and what is the optimal such φ when one exists?

DOI : 10.1016/j.anihpc.2012.12.011
Classification : 35B09, 35B33, 35B40, 35B44, 35B45, 35R45, 35J30, 35J91
Mots clés : Isolated singularity, Polyharmonic, Blow-up, Pointwise bound
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     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},
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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/

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