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arXiv · 1511.03188

Pointwise estimates of solutions to semilinear elliptic equations and inequalities

Alexander Grigor'yan·Igor Verbitsky
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Abstract

We obtain sharp pointwise estimates for positive solutions to the equation $-Lu+Vu^q=f$, where $L$ is an elliptic operator in divergence form, $q\in\mathbb{R}\setminus \{0\}$, $f\geq 0$ and $V$ is a function that may change sign, in a domain $Ω$ in $\mathbb{R}^{n}$, or in a weighted Riemannian manifold.

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Alexander Grigor'yan, Igor Verbitsky. 2015-11-10. Pointwise estimates of solutions to semilinear elliptic equations and inequalities. https://doi.org/10.1007/s11854-019-0004-z

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