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.
| 元の言語 | 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 |
| 発行部数 | SUPPL. |
| 出版物ステータス | Published - 2007 9 |
| 外部発表 | Yes |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Analysis
これを引用
Partial flat core properties associated to the p-Laplace operator. / Takeuchi, Shingo.
：: Discrete and Continuous Dynamical Systems- Series A, 番号 SUPPL., 09.2007, p. 965-973.研究成果: Article
}
TY - JOUR
T1 - Partial flat core properties associated to the p-Laplace operator
AU - Takeuchi, Shingo
PY - 2007/9
Y1 - 2007/9
N2 - 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.
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.
KW - Coincidence set
KW - Flat core
KW - P-Laplace operator
KW - Quasilinear elliptic equation
UR - http://www.scopus.com/inward/record.url?scp=70349901364&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=70349901364&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:70349901364
SP - 965
EP - 973
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
SN - 1078-0947
IS - SUPPL.
ER -