Does the Poisson Equation Have a Unique Solution with Mixed Boundary Conditions?

[ajeet mishra]

My professor told that poission equation has a unique solution even for mixed boundary conditions( i.e. Dirichlet bc for some part and Neumann for the remaining part). But how is this possible? As different boundary conditions for the same problem will give different solutions.

 

[Chestermiller]

My professor told that poission equation has a unique solution even for mixed boundary conditions( i.e. Dirichlet bc for some part and Neumann for the remaining part). But how is this possible? As different boundary conditions for the same problem will give different solutions.

It has a unique solution for each specified set of boundary conditions.

 

[ajeet mishra]

It has a unique solution for each specified set of boundary conditions.

But how? As there are unique solutions for drichlet and neumann conditions separately and these, in general, may not be consistent.

 

[Chestermiller]

But how? As there are unique solutions for drichlet and neumann conditions separately and these, in general, may not be consistent.

Can you provide a specific example (or examples) to illustrate what you are saying?