Doest sorting accept a dynamic programming solution?
Dynamic programming is an algorithmic technique, algorithms are classified as dynamic programming according to what their high-level structure "looks like", not according to a formal definition. If you really wanted to, you could force some sorting algorithms to fit into the dynamic-programming paradigm.

Let $A[1:n]$ be the array to sort, assume for simplicity that all its elements are distinct, and define $OPT[i]$ as the sorted array containing the smallest $i$ elements of $A$. 

According to this definition $OPT[0]$ is the empty array and, if you solve the subproblems in increasing order of $i$, you can recombine them as follows:

$$\displaystyle \forall i=1,\dots,n  \quad\quad OPT[i] = OPT[i-1] \circ \min_{x \in A \setminus OPT[i-1]} x,$$

where $\circ$ denotes concatenation. The optimal solution is in $OPT[n]$. Computing any $OPT[i]$ requires $O(n)$ time, therefore the total time needed is $O(n^2)$. At any point in time, you only need to store one $OPT[i]$, so the space complexity is $O(n)$.

This is essentially an ugly way to describe selection sort.