Approximation of elliptic equations with interior single-point degeneracy and its application to weak unique continuation property

Key Points

• This research aims to explore the weak unique continuation property for high-dimensional elliptic equations with interior degeneracy.
• Established well-posedness in weighted function spaces.
• Developed an innovative approximation method.
• Derived the three sphere inequality at the degenerate point.
• Applied the three sphere inequality to prove WUCP for two different cases.
• Demonstrated well-posedness for the class of elliptic equations in consideration.
• Validated the three sphere inequality at degenerate points.
• Proved the weak unique continuation property in two different scenarios.