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We are interested in path-dependent semilinear PDEs, where the derivativesare of G{\^a}teaux type in specific directions k and b, being the kernelfunctions of a Volterra Gaussian process X. Under some conditions on k, b andthe coefficients of the PDE, we prove existence and uniqueness of a decoupledmild solution, a notion introduced in a previous paper by the authors. We alsoshow that the solution of the PDE can be represented through BSDEs where theforward (underlying) process is X.

G{\^a}teaux type path-dependent PDEs and BSDEs with Gaussian forward processes