Lei Ouyang

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math.FA2024

Differential equations defined by Kre\uın-Feller operators on Riemannian manifolds

Sze-Man Ngai, Lei Ouyang

We study linear and semi-linear wave, heat, and Schrödinger equations defined by Kre\uın-Feller operator $- Δ_{μ}$ on a complete Riemannian $n$ -manifolds $M$ , where $μ$ is a finite po…

math.FA2024

Hodge Theorem for Krein-Feller operators on compact Riemannian manifolds

Sze-Man Ngai, Lei Ouyang

For an open set in a compact smooth oriented Riemannian n-manifold and a positive finite Borel measure with support contained in the closure of the open set, we define an associate…