Serrin-type problem in divergence form on Riemannian manifolds

Key Points

• Proving that equality leads to isometric domains resembles classic results in riemannian geometry, enhancing understanding.
• The investigation employs integral identities and the P-function method, demonstrating their utility in geometric inequalities.
• Exploring these problems under non-negative ricci curvature, we extend traditional symmetry concepts into broader geometric contexts.
• The findings indicate significant implications for boundary value problems in geometrically complex environments like riemannian manifolds.