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?