/sci/ - Science & Math » Thread #14260009

27KiB, 1200x1520, lagrange.png

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Lagrange Problem

Anonymous Thu 24 Feb 00:37:11 2022 No.14260009 View Reply Original Report

Quoted By: >>14260059

First off this is NOT a homework problem it was just a hypothetical example I came up with

Second how do I solve the Lagrange Equation in this region? I asked my professor this and we couldn't figure it out

Anonymous

Anonymous Thu 24 Feb 2022 00:45:17 No.14260035 Report

Quoted By: >>14260060

I have no idea what this drawing represents

Anonymous

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Anonymous Thu 24 Feb 2022 00:53:46 No.14260059 Report

Quoted By:

>>14260009
Do you seriously think we can tell whatever the fuck you mean?
My best guess is $y = \dot{x}$ and your Lagrangian is the characteristic function of $[0, b] \times [0, a]$ times $V_a$ .

Anonymous

Anonymous Thu 24 Feb 2022 00:53:48 No.14260060 Report

Quoted By: >>14260070

>>14260035
sorry, it's a square (obviously) where the potential is some value v naught on the upper and left edges and zero on the right and bottom edges. the edges are a and b long (could just be a and a)
The question is how do you solve the lagrange equation in that square? if you don't know the lagrange equation in two dimensions is just *second partial of v with respect to x* + *second partial of v with respect to y* = 0 where v is electric potential

Anonymous

Anonymous Thu 24 Feb 2022 00:56:59 No.14260070 Report

Quoted By: >>14260077 >>14260080

>>14260060
>if you don't know the lagrange equation in two dimensions is just *second partial of v with respect to x* + *second partial of v with respect to y* = 0 where v is electric potential
Did you seriously write Lagrange instead of Laplace?

Anonymous

Anonymous Thu 24 Feb 2022 01:02:18 No.14260077 Report

Quoted By: >>14260092

>>14260070
fuck

Anonymous

Anonymous Thu 24 Feb 2022 01:03:18 No.14260080 Report

Quoted By: >>14260092

>>14260070
mods please delete this thread im embarrased

Anonymous

Anonymous Thu 24 Feb 2022 01:09:52 No.14260092 Report

Quoted By:

>>14260077
>>14260080
Right, right, basically, you want to solve Laplace with non-continuous boundary conditions?
You can't. Solutions of Laplace are all smooth. Including weak solutions of all sorts. Basic elliptic regularity.

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