Partial flat core properties associated to the p-Laplace operator

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)965-973
Number of pages9
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue numberSUPPL.
Publication statusPublished - 2007 Sep
Externally publishedYes

Keywords

  • Coincidence set
  • Flat core
  • P-Laplace operator
  • Quasilinear elliptic equation

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Partial flat core properties associated to the p-Laplace operator. / Takeuchi, Shingo.

In: Discrete and Continuous Dynamical Systems- Series A, No. SUPPL., 09.2007, p. 965-973.

Research output: Contribution to journalArticle

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AB - 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.

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