Title
Weak solutions to Serrin's overdetermined problem
Abstract
Serrin's classical overdetermined theorem states that if a bounded C^2-domain supports a function with a constant Laplacian that satisfies both constant Dirichlet and Neumann boundary conditions, then the domain must be a ball. In this presentation, we explore this problem further, demonstrating that the theorem's conclusion extends to a broader class of domains, including Lipschitz domains. Our method is based on theory from geometric measure theory and harmonic analysis.
