Can a mixed derivative be used to specify a boundary condition?

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Let’s say I have Partial Differential Equation

$$f_{xxy}(x,y) + f_{y}(x,y)+f(x,y)=0$$

Can I specify a boundary condition of the type

$$f_{xy}(0,0)=0$$

Or something similar?

I have looked online and for the limited content I’ve found on third order or higher Partial Differential Equations, I haven’t found anything about the type of boundary conditions specified above. Can a mixed derivative be used to specify a boundary condition?