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A priori bounds for a class of semi-linear degenerate elliptic equations

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Abstract

In this paper, we mainly discuss a priori bounds of the following degenerate elliptic equation,

$$a^{ij} (x)\partial _{ij} u + b^i (x)\partial _i u + f(x,u) = 0, in \Omega \subset \subset \mathbb{R}^n ,$$
(1)

where a ij ∂ i ϕ∂ j ϕ = 0 on ∂Ω, and ϕ is the defining function of ∂Ω. Imposing suitable conditions on the coefficients and f(x, u), one can get the L ∞-estimates of (*) via blow up method.

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  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    GengGeng Huang

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  1. GengGeng Huang
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Huang, G. A priori bounds for a class of semi-linear degenerate elliptic equations. Sci. China Math. 57, 1911–1926 (2014). https://doi.org/10.1007/s11425-014-4770-x

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