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arXiv · 1502.03271

On singular elliptic equations with measure sources

Francescantonio Oliva·Francesco Petitta
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Abstract

We prove existence of solutions for a class of singular elliptic problems with a general measure as source term whose model is $$\begin{cases} -Δu = \frac{f(x)}{u^γ} +μ& \text{in}\ Ω, u=0 &\text{on}\ \partialΩ, u>0 &\text{on}\ Ω, \end{cases} $$ where $Ω$ is an open bounded subset of $\mathbb{R}^N$. Here $γ> 0$, $f$ is a nonnegative function on $Ω$, and $μ$ is a nonnegative bounded Radon measure on $Ω$.

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Francescantonio Oliva, Francesco Petitta. 2017-02-14. On singular elliptic equations with measure sources. https://doi.org/10.1051/cocv%2F2015004

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