TY - JOUR
T1 - Partial flat core properties associated to the p-Laplace operator
AU - Takeuchi, Shingo
PY - 2007/9/1
Y1 - 2007/9/1
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
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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 -