Chris Donlan
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 Sep24 awarded Autobiographer Oct20 comment Green's Formula as proof for harmony Results of chat: Tomas identified a couple of issues with the application of the Green Identity...and so I tried to account for that by applying the Green Identity to a region whose perimeter did not include the origin (and, consequently, a singularity)...don't know if it is allowed though (or procedurally correct. Thanks Tomas. Oct18 revised Green's Formula as proof for harmony added 111 characters in body Oct18 revised Green's Formula as proof for harmony added 524 characters in body Oct18 revised Green's Formula as proof for harmony included the origin in Green's Formula integrals Oct18 comment Green's Formula as proof for harmony as to measurability, looking at this it seems like the set of $x\in \Omega '$ encompasses every vector $\gt 0$...so I guess it is measurable. Oct18 comment Green's Formula as proof for harmony (2): if $\{0\}$ is in the domain, $\frac{1}{|x|}$ becomes a singularity. It is likely dumped to guarantee smoothness.  (1): Use of the ball mean property is required for the "correct answer." Any function satisfying the mean value property must be smooth, according to the proof... it is sufficient that it be locally integrable and measurable in $\Omega$. Since $\bar{\mu} \in \Omega$, it is locally integrable...because u is locally integrable in $\Omega$. Oct18 revised Green's Formula as proof for harmony added 95 characters in body Oct18 awarded Supporter Oct18 revised Green's Formula as proof for harmony added 80 characters in body Oct18 answered The free-space Green's function for the Stokes flow Oct18 revised Green's Formula as proof for harmony split a line of math into two lines for readability; fixed grammar Oct18 revised Green's Formula as proof for harmony split a line of math into two lines for readability Oct18 asked Green's Formula as proof for harmony Oct18 awarded Peer Pressure Oct16 comment PDE: Maximum principle + Periodic Boundary Conditions = Constant? Ok, thanks, I'll try that. Oct16 accepted PDE: Maximum principle + Periodic Boundary Conditions = Constant? Oct16 comment PDE: Maximum principle + Periodic Boundary Conditions = Constant? I really appreciate the help. I was stuck, big time. Oct16 comment PDE: Maximum principle + Periodic Boundary Conditions = Constant? @Sam, Yeah, I think it will follow from the 1D example. I re-read your post. My mistake on the other two comments. Forgot that you accounted for $C^2$ as versus $C^{\infty}$... Oct16 comment PDE: Maximum principle + Periodic Boundary Conditions = Constant? LOL. Getting there. There must be a interior maximum or minimum such that $f'(x)=0$ in order for $f(a)=f(b)$...and, in order for $f''(x)=0$, the rest of the values in between the critical point $f'(x)=0$ and $a$ and $b$, they must be either constant or zero... But if they are non-zero constants, then continuity is broken at the point $f'(x)=0$ and therefore they must be zero, making $f(x)=constant$.