Hi,

the same command does not evaluate inMathematica 9 and gives an error message instead:

NDSolveValue::ivone: Boundary values may only be specified for one independent variable. Initial values may only be specified at one value of the other independent variable. >>

Also, if you invert the sign of your first condition like this:

uif = NDSolveValue[D[f[x, y], {x, 2}] + D[f[x, y], {y, 2}] == 1 && Derivative[1, 0][f][1, y] == -1 && f[0, y] == 1, f, {x, 0, 1}, {y, 0, 1}]

you get a positive 1 derivative just as you wanted.

Plot3D[uif[x, y], {x, 0, 1}, {y, 0, 1}]

I know that this does not solve your problem. I am not really sure what MMA10 does differently from MMA9 here.

Cheers, Marco