Pointwise bounds and blow-up for nonlinear polyharmonic inequalities
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 6, p. 1069-1096

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?

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 ?

DOI : https://doi.org/10.1016/j.anihpc.2012.12.011
Classification:  35B09,  35B33,  35B40,  35B44,  35B45,  35R45,  35J30,  35J91
Keywords: 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},
     publisher = {Elsevier},
     volume = {30},
     number = {6},
     year = {2013},
     pages = {1069-1096},
     doi = {10.1016/j.anihpc.2012.12.011},
     zbl = {1286.35278},
     mrnumber = {3132417},
     language = {en},
     url = {http://www.numdam.org/item/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, Volume 30 (2013) no. 6, pp. 1069-1096. doi : 10.1016/j.anihpc.2012.12.011. http://www.numdam.org/item/AIHPC_2013__30_6_1069_0/

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