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L.F. Cavenaghi
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Is $\int_M\Delta u = 0$ if $u$ is not $C^2$ on a set of measure zero?

Suppose that $M$ is a closed Riemannian manifold and that $u$ is a $C^2$ function on almost every point. Can we still conclude that $\int_M\Delta u =0?$

L.F. Cavenaghi
  • 1.8k
  • 11
  • 17