Timeline for A Liouville theorem for a uniformly elliptic equation in divergence form

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when toggle format	what		by	license	comment
Mar 23, 2018 at 9:50	vote	accept	Onil90
Mar 23, 2018 at 9:43	comment	added	Onil90		@JochenGlueck Nice example! Thanks!
Mar 22, 2018 at 15:18	comment	added	Jochen Glueck		It might be instructive to add the following concrete example: if we drop the condition that $b$ be smooth, we can choose $b(x) = \operatorname{sgn}(x)$ and consider the equation $u''(x) + \operatorname{sgn}(x) u'(x) = 0$ in the sense of distributions. This equation is solved by all constant functions and by the $H^1$-function $\tilde u$ given by $\tilde u(x) = 1 - e^{-x}$ for $x \ge 0$ and $u(x) = e^x - 1$ for $x < 0$.
Mar 22, 2018 at 13:13	history	answered	R W	CC BY-SA 3.0