In a polynomial ring over a perfect field, the symbolic powers of a radical ideal consist of the polynomials that vanish to order n on the corresponding variety, and can be described via differential operators. If we replace the field with a DVR, we need both differential operators and Joyal and Buium's notion of a p-derivation to give an analogous result. As an application, we will discuss an explicit Chevalley lemma for the symbolic powers of prime ideals in direct summands of polynomial rings. This is joint work with Alessandro De Stefani and Jack Jeffries.