Differential and Integral Equations

A Lazer-Mckenna type problem with measures

Luigi Orsina and Francesco Petitta

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In this paper, we are concerned with a general singular Dirichlet boundary value problem whose model is the following: $$ \begin{cases} -\Delta u = \frac{\mu}{u^{\gamma}} & \text{in}\ \Omega,\\ u=0 &\text{on}\ \partial\Omega,\\ u>0 &\text{on}\ \Omega\,. \end{cases} $$ Here, $\mu$ is a nonnegative bounded Radon measure on a bounded open set $\Omega\subset\mathbb R^N$, and $\gamma>0$.

Article information

Differential Integral Equations, Volume 29, Number 1/2 (2016), 19-36.

First available in Project Euclid: 24 November 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J60: Nonlinear elliptic equations 35J61: Semilinear elliptic equations 35J75: Singular elliptic equations 5R06


Orsina, Luigi; Petitta, Francesco. A Lazer-Mckenna type problem with measures. Differential Integral Equations 29 (2016), no. 1/2, 19--36. https://projecteuclid.org/euclid.die/1448323251

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