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location Atlanta, GA
age 27
visits member for 2 years, 7 months
seen Oct 30 '12 at 3:05

Currently a grad student. Taking a course in PDE.


Oct
20
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.
Oct
18
revised Green's Formula as proof for harmony
added 111 characters in body
Oct
18
revised Green's Formula as proof for harmony
added 524 characters in body
Oct
18
revised Green's Formula as proof for harmony
included the origin in Green's Formula integrals
Oct
18
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.
Oct
18
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 $\Omega$.
Oct
18
revised Green's Formula as proof for harmony
added 95 characters in body
Oct
18
awarded  Supporter
Oct
18
revised Green's Formula as proof for harmony
added 80 characters in body
Oct
18
answered The free-space Green's function for the Stokes flow
Oct
18
revised Green's Formula as proof for harmony
split a line of math into two lines for readability; fixed grammar
Oct
18
revised Green's Formula as proof for harmony
split a line of math into two lines for readability
Oct
18
asked Green's Formula as proof for harmony
Oct
18
awarded  Peer Pressure
Oct
16
comment PDE: Maximum principle + Periodic Boundary Conditions = Constant?
Ok, thanks, I'll try that.
Oct
16
accepted PDE: Maximum principle + Periodic Boundary Conditions = Constant?
Oct
16
comment PDE: Maximum principle + Periodic Boundary Conditions = Constant?
I really appreciate the help. I was stuck, big time.
Oct
16
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 $C^{\infty}$...
Oct
16
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 $f(x)=constant$.
Oct
16
revised PDE: Maximum principle + Periodic Boundary Conditions = Constant?
added 2 characters in body