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1. Invariant elliptic estimates

Author

Cho, Yonggeun, Ozawa, Tohru, and Shim, Yong-Sun

Subjects
*ELLIPTIC functions, *INVARIANTS (Mathematics), *LAME'S functions, *ESTIMATION theory, *MATHEMATICS, *MATHEMATICAL analysis
Abstract

Abstract: In this paper, we revisit elliptic estimates invariant under domain expansion. We improve the invariant elliptic estimates in the previous paper [Y. Cho, T. Ozawa, Y. Shim, Calc. Var. PDE 34 (2009) 321–339] via gradient estimate and discuss an application to the Lamé system. [Copyright &y& Elsevier]

Published
2011
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2. Convexity of the complete elliptic integrals of the first kind with respect to Hölder means

Author

Wang, Miao-Kun, Chu, Yu-Ming, Qiu, Song-Liang, and Jiang, Yue-Ping

Subjects
*CONVEX domains, *ELLIPTIC functions, *HYPERELLIPTIC integrals, *SUFFICIENT statistics, *MATHEMATICAL analysis, *MATHEMATICS
Abstract

Abstract: In this paper, we establish a necessary and sufficient condition for the convexity of the complete elliptic integrals of the first kind with respect to Hölder means. [Copyright &y& Elsevier]

Published
2012
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3. A note on positive evanescent solutions for a certain class of elliptic problems

Author

Djebali, Smaïl and Orpel, Aleksandra

Subjects
*ELLIPTIC differential equations, *ELLIPTIC functions, *NONLINEAR theories, *ASYMPTOTES, *MATHEMATICAL analysis, *MATHEMATICS
Abstract

Abstract: This paper is devoted to the existence and properties of solutions of the following class of nonlinear elliptic differential equations , , . We prove existence of positive solutions vanishing at positive infinity. Our approach is based on the subsolution and supersolution method. The nonlinearity f covers both sublinear and superlinear cases and does not necessarily satisfy . The asymptotic behavior of solutions is also described. [Copyright &y& Elsevier]

Published
2009
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