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Elio Li
Elio Li
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Maybe Theorem 4.8 in Thierry Aubin - Some Nonlinear Problems in Riemannian Geometry will help. It said that

let $\bar{W}_n$ be a compact Riemannian manifold with boundary of, then there exists a solution $\varphi \in C^{\infty}(\bar{W}_n)$ of $$\Delta \varphi =f$$ here $f$ is smooth and $\varphi$ vanishes on the boundary.

Maybe Theorem 4.8 in Thierry Aubin - Some Nonlinear Problems in Riemannian Geometry will help. It said that

let $\bar{W}_n$ be a compact Riemannian manifold with boundary of then there exists a solution $\varphi \in C^{\infty}(\bar{W}_n)$ of $$\Delta \varphi =f$$ here $f$ is smooth and $\varphi$ vanishes on the boundary.

Maybe Theorem 4.8 in Thierry Aubin - Some Nonlinear Problems in Riemannian Geometry will help. It said that

let $\bar{W}_n$ be a compact Riemannian manifold with boundary, then there exists a solution $\varphi \in C^{\infty}(\bar{W}_n)$ of $$\Delta \varphi =f$$ here $f$ is smooth and $\varphi$ vanishes on the boundary.

Source Link
Elio Li
Elio Li
  • 809
  • 4
  • 13

Maybe Theorem 4.8 in Thierry Aubin - Some Nonlinear Problems in Riemannian Geometry will help. It said that

let $\bar{W}_n$ be a compact Riemannian manifold with boundary of then there exists a solution $\varphi \in C^{\infty}(\bar{W}_n)$ of $$\Delta \varphi =f$$ here $f$ is smooth and $\varphi$ vanishes on the boundary.