  We show that the Born-Infeld action with the Wess-Zumino terms for the
Ramond-Ramond fields, which is the D3-brane effective action, is a solution to
the Hamilton-Jacobi (H-J) equation of type IIB supergravity. Adopting the
radial coordinate as time, we develop the ADM formalism for type IIB
supergravity reduced on $S^5$ and derive the H-J equation, which is the
classical limit of the Wheeler-De Witt equation and whose solutions are
classical on-shell actions. The solution to the H-J equation reproduces the
on-shell actions for the supergravity solution of a stack of D3-branes in a
$B_2$ field and the near-horizon limit of this supergravity solution, which is
conjectured to be dual to noncommutative Yang Mills and reduces to $AdS_5
\times S^5$ in the commutative limit. Our D3-brane effective action is that of
a probe D3-brane, and the radial time corresponds to the vacuum expectation
value of the Higgs field in the dual Yang Mills. Our findings can be applied to
the study of the holographic renormalization group.
