On a singular nonlinear elliptic boundary-value problem

Lazer, A. C.; McKenna, P. J.

doi:10.1090/S0002-9939-1991-1037213-9

On a singular nonlinear elliptic boundary-value problem
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by A. C. Lazer and P. J. McKenna PDF

Proc. Amer. Math. Soc. 111 (1991), 721-730 Request permission

Abstract:

We consider the singular boundary-value problem $\Delta u + p(x){u^{ - \gamma }} = 0$ in $\Omega ,u|\partial \Omega = 0$, where $\gamma > 0$. Under the assumption $p(x) > 0$ and certain smoothness assumptions, we show that there exists a solution which is smooth on $\Omega$ and continuous on $\bar \Omega$.

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