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Timeline for Pde system problem

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Nov 15, 2017 at 11:53 vote accept MathDG
Nov 15, 2017 at 10:36 answer added Robert Bryant timeline score: 12
Nov 15, 2017 at 10:12 comment added Igor Khavkine @exxxit8, all these different cases are quite similar. So if you don't understand the $c\ne 0$ case, I'm sorry to say, then you probably don't understand the other cases either. What you should do first is thoroughly understand the cases where the solution is known.
Nov 15, 2017 at 6:44 comment added MathDG @Igor Khavkine, thank you very much, but I don't understand for $c$ not zero.
Nov 15, 2017 at 6:42 comment added MathDG @Alexander Pigazzini, thank you very much
Nov 15, 2017 at 6:15 comment added MathDG @exxxit8, for exemple $h=c=0$ implies $f$ harmonic, and the result is the same for $h \neq 0$ and $c=0$, i.e. $h \neq 0$ and $f=0$, or $h=0$ and $f=$constant.
Nov 15, 2017 at 1:21 comment added Igor Khavkine @exxxit8, I strongly encourage you to first work through the steps of the $h=c=0$ and $c=0,h\ne 0$ cases, and then apply the same method to the $c\ne 0$ case.
Nov 14, 2017 at 21:46 history edited MathDG CC BY-SA 3.0
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Nov 14, 2017 at 19:19 comment added Ben McKay If you have two different questions, why not ask them separately? It will be easier to understand the questions and the answers if you ask the questions separately.
Nov 14, 2017 at 19:18 vote accept MathDG
Nov 15, 2017 at 11:53
Nov 14, 2017 at 19:13 answer added Igor Khavkine timeline score: 3
Nov 14, 2017 at 18:42 comment added MathDG @Willie Wong, No, are two separate case.. I said that badly, sorry!
Nov 14, 2017 at 18:23 comment added Willie Wong I don't understand your question, you have a system of two PDEs about a scalar function $f$ (which means surely your system is overdetermined). But then you say that simultaneously $f$ is defined on $\mathbb{R}^2$ and a surface $S$: which is it?
Nov 14, 2017 at 16:46 comment added MathDG @Chris Ramsey, I found a particular manifold with Einstein condition in isotropic space... $f$ is defined on surface and it is a positive scalar function
Nov 14, 2017 at 16:42 history edited MathDG CC BY-SA 3.0
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Nov 14, 2017 at 16:39 comment added Chris Ramsey Please give some context as to why you are interested in this problem.
Nov 14, 2017 at 16:08 review First posts
Nov 14, 2017 at 16:39
Nov 14, 2017 at 16:05 history asked MathDG CC BY-SA 3.0