Partial flat core properties associated to the p-Laplace operator

研究成果: Article査読

5 被引用数 (Scopus)

抄録

This paper deals with singular perturbation problems for quasilin-ear elliptic equations with the p-Laplace operator, e.g., - εδ pu = up-1 \a(x) - u\q-1 (a(x) - u), where ε is a positive parameter, p > 1, q > 0 and a(x) is a positive continuous function. It is proved that any positive solution converges to a(x) uniformly in any compact subset as ε → 0. In particular, when q < p- 1 and ε is small enough, the solutions coincide with a(x) on one or more than one subdomain where a(x) is constant, and hence there appear flat cores partially in the whole domain. These results are proved by comparison principles.

本文言語English
ページ(範囲)965-973
ページ数9
ジャーナルDiscrete and Continuous Dynamical Systems- Series A
SUPPL.
出版ステータスPublished - 2007 9月 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 離散数学と組合せ数学
  • 応用数学

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