Boundary Conditions of a Stepped Beam

I would like to ask about the boundary conditions to be considered in a stepped beam. For a cantilever beam wherein the one end is fixed while the other end is free to oscillate along the z-axis, we can set the deflection equation to be W(x). The boundary conditions at the fixed end are W(0)=0 and W'(0)=0 while at the free end, W”(L)=0 and W”'(L)=0.

I would just like to ask about the boundary conditions or continuity equations that will exist at x=L1, or the boundary between the thick beam and the thin beam. What underlying equations will exist here?

Thanks a lot for your information. 🙂