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1999 Elliptic equations with singularity on the boundary
Satoshi Hashimoto, Mitsuharu Ôtani
Differential Integral Equations 12(3): 339-349 (1999).

Abstract

The existence and nonexistence of positive classical solutions is discussed for $-\Delta u = K(x) (1-|x|)^{- \alpha} u^{\beta}$ in the unit ball $B$ with Dirichlet boundary condition ${u |_{\partial B}= 0 }$. Our main tools are based on the variational method and Pohozaev's identity. The singularity of coefficients on the boundary will be handled with the symmetry of functions and some approximation procedures.

Citation

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Satoshi Hashimoto. Mitsuharu Ôtani. "Elliptic equations with singularity on the boundary." Differential Integral Equations 12 (3) 339 - 349, 1999.

Information

Published: 1999
First available in Project Euclid: 29 April 2013

zbMATH: 1053.35048
MathSciNet: MR1674402

Subjects:
Primary: 35J65

Rights: Copyright © 1999 Khayyam Publishing, Inc.

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Vol.12 • No. 3 • 1999
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