# Questions tagged [partial-differential-equations]

Questions on partial (as opposed to ordinary) differential equations - equations involving partial derivatives of one or more dependent variables with respect to more than one independent variables.

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### Integration by parts of 3 vectorial functions

I am considering the following integral $$\int_{\mathbb{R}^d} ( [\nabla a ]\cdot \nabla b ) \Delta c \ dx,$$ with $a, b$ and $c$ vanishing in the infinity. By considering integration by parts,...
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### How to solve spinorial differential equations.

I've asked this question in the Physics Exchange Forums, but I think this is a more appropaite site to ask this question. How would you solve the following differential equation, and find its ...
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### Is the weak derivative a Radon-Nikodym derivative?

It seems reasonable to me to conjecture that the weak derivative is a special case of Radon-Nikodym derivative between measures. Recall that (missing some technical details): Weak derivative: given a ...
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### Show that $\{p,\{p,\phi\}\}>0$ on $T_{\Sigma}^{*}\mathbb{R}^{n}$
I am reading an article and I found the following situation, Suppose we have a differential operator $P(x,D)$ of order $m$ in $\mathbb{R}^n$. Let $\Sigma$ be an oriented hypersurface in $\mathbb{R}^n$,...