Characterizing the Strong Maximum Principle
arXiv:1309.1738
Abstract
In this paper we characterize the degenerate elliptic equations F(D^2u)=0 whose viscosity subsolutions, (F(D^2u) \geq 0), satisfy the strong maximum principle. We introduce an easily computed function f(t) for t > 0, determined by F, and we show that the strong maximum principle holds depending on whether the integral \int dy / f(y) near 0 is infinite or finite. This complements our previous work characterizing when the (ordinary) maximum principle holds. Along the way we characterize radial subsolutions.
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