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A priori estimates of positive solutions for sublinear elliptic equations
Author(s):
Ryuji
Kajikiya
Journal:
Trans. Amer. Math. Soc.
361
(2009),
3793-3815.
MSC (2000):
Primary 35B45, 35J25;
Secondary 35J65
Posted:
February 10, 2009
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Abstract:
In this paper, a priori estimates of positive solutions for sublinear elliptic equations are given in terms of thicknesses of domains. To this end, a supersolution is constructed by a composite function of a solution to an ordinary differential equation and a distance function. The results work efficiently in the case where the domain is an exterior or an interior of a convex set.
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Additional Information:
Ryuji
Kajikiya
Affiliation:
Nagasaki Institute of Applied Science, 536 Aba-machi, Nagasaki 851-0193, Japan
Address at time of publication:
Department of Mathematics, Faculty of Science and Engineering, Saga University, Saga, 840-8502, Japan
Email:
kajikiya_ryuji@nias.ac.jp, kajikiya@ms.saga-u.ac.jp
DOI:
10.1090/S0002-9947-09-04875-2
PII:
S 0002-9947(09)04875-2
Keywords:
Sublinear elliptic equation,
a priori estimates,
thickness of domain,
positive solution
Received by editor(s):
August 10, 2007
Posted:
February 10, 2009
Additional Notes:
This work was supported in part by the Grant-in-Aid for Scientific Research (C) (No. 20540197), Ministry of Education in Japan.
Copyright of article:
Copyright
2009,
American Mathematical Society
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