Differential and Integral Equations

Elliptic equations with singularity on the boundary

Satoshi Hashimoto and Mitsuharu Ôtani

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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.

Article information

Source
Differential Integral Equations, Volume 12, Number 3 (1999), 339-349.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367265215

Mathematical Reviews number (MathSciNet)
MR1674402

Zentralblatt MATH identifier
1053.35048

Subjects
Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations

Citation

Hashimoto, Satoshi; Ôtani, Mitsuharu. Elliptic equations with singularity on the boundary. Differential Integral Equations 12 (1999), no. 3, 339--349. https://projecteuclid.org/euclid.die/1367265215


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