MathGroup Archive 2003

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: elliptic equation solved with 2 boundaries

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43381] Re: [mg43294] elliptic equation solved with 2 boundaries
  • From: Selwyn Hollis <selwynh at earthlink.net>
  • Date: Wed, 27 Aug 2003 04:05:07 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Sorry, I should have read your reply more carefully... Let's have 
another go at this.

On Tuesday, August 26, 2003, at 09:20  AM, Ferdinand.Cap wrote:

> Hi,
> Thank you for your interest in my notebook.  The LAPLACE
>  equation has complex characteristics and is therfor called an elliptic
> partial differential eqatiuon.  The theory of boundary value problems
> (Table 1.1. on page 14 in the book mentioned in the notebook )shows
> that an elliptic partial differential equation   can only satisfy one
> boundary value probblem.

That is patent nonsense. First, equations don't satisfy boundary value 
problems, solutions do. Second, even the trivial case of a constant 
function satisfies both Dirichlet boundary conditions and Neumann 
boundary conditions on any domain you care to consider. Voila: two 
boundary value problems.

Perhaps you mean that a given elliptic equation (with smooth 
coefficients) subject to appropriate boundary conditions has a unique 
solution?

> My notebokk demonstrates that under special conditions
> also 2 boundary value problems can be satisfied - run the notebook!

When you say two boundary value problems, do you mean one with a 
two-part boundary? It appears from the notebook that that is what you 
really mean. I suggest you restudy the theory if you think that is 
something out of the ordinary.

> Due to the approoximation method -variational calculus - the LAPLACIAN 
> is
> not zero, but numerically small F.C

What do you mean by numerically small? A plot,

Plot3D[Evaluate[D[f[x, y], x, x] + D[f[x, y], y, y]],{x,-2,2},{y,-2,2}]

shows that the Laplacian is HUGE on the region where you seem to be 
claiming it's "numerically small". But then again, you never actually 
stated the problem you claimed to have solved, so who knows...

-----
Selwyn Hollis
http://www.math.armstrong.edu/faculty/hollis


  • Prev by Date: Re: Define a function and its derivatives
  • Next by Date: Re: New version, new bugs
  • Previous by thread: elliptic equation solved with 2 boundaries
  • Next by thread: Re: elliptic equation solved with 2 boundaries