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- How to determine the boundary conditions to this elliptic BVP given an analytical solution

For this BVP in ##(0,1)^2##,

$$

-u_{xx} - u_{yy} = 0

$$

subject to some boundary data it is said the analytical solution is ##u(x,y) = \theta##. I've thought about this for awhile I can't seem to figure out how to determine the boundary conditions for this BVP. Moreover, ##\theta## is illustrated in figure attached. Some comments would be greatly appreciated.

$$

-u_{xx} - u_{yy} = 0

$$

subject to some boundary data it is said the analytical solution is ##u(x,y) = \theta##. I've thought about this for awhile I can't seem to figure out how to determine the boundary conditions for this BVP. Moreover, ##\theta## is illustrated in figure attached. Some comments would be greatly appreciated.