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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A priori estimates of positive solutions for sublinear elliptic equations


Author: Ryuji Kajikiya
Journal: Trans. Amer. Math. Soc. 361 (2009), 3793-3815
MSC (2000): Primary 35B45, 35J25; Secondary 35J65
Published electronically: February 10, 2009
MathSciNet review: 2491900
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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: http://dx.doi.org/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
Published electronically: 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.
Article copyright: © Copyright 2009 American Mathematical Society