Parabolic equations on conic manifolds - Sulez, Weymar Andrés Astaiza (2024)
We are going to present results about parabolic equations on conic manifolds using Lp and continuous functions. First, we show existence of global solutions for a typical Reaction-Diffusion equation on a conic manifold B. We consider Mellin-Sobolev spaces. These are function spaces built using Lp norms. Second, we show sectoriality for elliptic differential and pseudodifferential operators acting on continuous spaces on compact manifolds without boundary and without conical points. Third, for a conic manifold B, we extend the continuous and C1 spaces and we show that elliptic differential operators define almost sectorial operators on these spaces.