What Is the Physical Meaning of Laplace Equations in Higher Dimensions?

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it's konwn to all that laplace equation in 3 dimentions have clearly physical meaning,how about that in higher dimentions?
I first thought that had something to do with relativity or quantum mechenics with higher dimentions ,but it is hard to figure it out .
can anybody explain that ,thanks a lot
 
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If you are thinking in term of physical meaning, the only additional dimension that I can imagine is the time dimension. So we have the space-time dimension. Is is possible to have four space dimension ?
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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