Pointwise bounds and blow-up for nonlinear polyharmonic inequalities

  • Steven D. Taliaferro

    Mathematics Department, Texas A&M University, College Station, TX 77843-3368, United States

Abstract

We obtain results for the following question where and are integers.

Question. For which continuous functions does there exist a continuous function such that every nonnegative solution of

satisfies

and what is the optimal such when one exists?

Résumé

Nous obtenons des résultats pour la question suivante, avec et entiers.

Question. Pour quelles fonctions continues existe-t-il une fonction continue telle que chaque solution non-negative de

satisfasse à

et quelle est la meilleure de ces fonctions quand elle existe ?

Cite this article

Steven D. Taliaferro, Pointwise bounds and blow-up for nonlinear polyharmonic inequalities. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 6, pp. 1069–1096

DOI 10.1016/J.ANIHPC.2012.12.011