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Boundary behavior of large viscosity solutions to infinity Laplace equations

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Abstract

In this paper, we give the structure conditions on two classes of functions f(u): one grows up at infinity faster than any u p (p > 3) and the other is normalized regularly varying at infinity with the critical index 3, and we show the new boundary behavior of boundary blow-up viscosity solutions to the equation \({\triangle_\infty u = b(x)f(u),\, u \geq 0, x \in \Omega,}\) where \({\Omega}\) is a bounded domain with smooth boundary in \({\mathbb R^N}\), the operator \({\triangle_\infty}\) is the \({\infty}\)-Laplacian, and \({b \in C(\bar{\Omega})}\) which is nonnegative in \({\Omega}\).

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  1. School of Mathematics and Information Science, Yantai University, Yantai, 264005, Shandong, People’s Republic of China

    Zhijun Zhang

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  1. Zhijun Zhang
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Correspondence to Zhijun Zhang.

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This work was supported in part by NNSF of P. R. China under Grant 11301301.

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Zhang, Z. Boundary behavior of large viscosity solutions to infinity Laplace equations. Z. Angew. Math. Phys. 66, 1453–1472 (2015). https://doi.org/10.1007/s00033-014-0470-1

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  • DOI: https://doi.org/10.1007/s00033-014-0470-1

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