応用解析セミナー

過去の記録 ~02/06次回の予定今後の予定 02/07~

開催情報 木曜日 16:00~17:30 数理科学研究科棟(駒場) 002号室
担当者 石毛 和弘

2019年10月31日(木)

16:00-17:30   数理科学研究科棟(駒場) 128 (TBD)号室
Marius Ghergu 氏 (University College Dublin)
Behaviour around the isolated singularity for solutions of some nonlinear elliptic inequalities and systems (English)
[ 講演概要 ]
We present some results on the behaviour around the isolated singularity for solutions of nonlinear elliptic inequalities driven by the Laplace operator. We derive optimal conditions that imply either a blow-up or the existence of pointwise bounds for solutions. We obtain that whenever a pointwise bound exists, then an optimal bound is given by the fundamental solution of the Laplace operator. This situation changes in case of systems of inequalities where other types of optimal bounds may occur. The approach relies on integral representation of solutions combined with various nonlinear potential estimates. Further extensions to the parabolic case will be presented. This talk is based on joint works with S. Taliaferro (Texas A&M University) and I. Verbitsky (Missouri University).