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arXiv · 1201.5801

Quantitative Local Bounds for Subcritical Semilinear Elliptic Equations

Matteo Bonforte·Gabriele Grillo·Juan Luis Vazquez
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Abstract

The purpose of this paper is to prove local upper and lower bounds for weak solutions of semilinear elliptic equations of the form $-Δu= c u^p$, with $0<p<p_s=(d+2)/(d-2)$, defined on bounded domains of $\RR^d$, $d\ge 3$, without reference to the boundary behaviour. We give an explicit expression for all the involved constants. As a consequence, we obtain local Harnack inequalities with explicit constant, as well as gradient bounds.

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Matteo Bonforte, Gabriele Grillo, Juan Luis Vazquez. 2012-01-27. Quantitative Local Bounds for Subcritical Semilinear Elliptic Equations. https://arxiv.org/abs/1201.5801

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