The p-sum for two convex bodies was introduced by Firey. The associated Brunn-Minkowski-Firey theory was later developed by Lutwak. In this talk, I will discuss the L^p Christoffel-Minkowski problem and focus on its PDE aspect. We will review previous results and prove that for the case $1<p<k+1$, if the given data is even and also satisfies certain convexity condition, then there exists a unique solution to this problem. We give examples to show the evenness condition cannot be removed in general. This is joint work in progress with Pengfei Guan.

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