Green Function of the Zaremba Problem for the Heat Operator

Key Points

• To prove the existence and uniqueness of the Green’s function for heat operator under specific boundary conditions.
• Considered a parabolic initial-boundary value problem
• Applied homogeneous Zaremba boundary conditions
• Focused on a cylinder with a Lipschitz bounded base domain
• Demonstrated the existence of the Green’s function
• Established uniqueness for the Green’s function under the specified conditions