Determine a partial differential equation bvp

Question

Solution to a Partial Differential Equation BVP

Explain in some detail, the reason for your answer:

For n > 0; find the solution to the boundary value problem -Δu=(n/π)e^-n(x2+y2),x²+y²<1,u(x,y)=0,x²+y2=1.
What happens in the limit as n →∞?(Δu=∂²u/∂x²+∂²u/∂y²)