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May 29, 2020 at 2:56 comment added Anton Petrunin @Doggyy Since Hessian is bounded, $|\nabla f|$ is Lipschitz. Therefore $f$ is Lipschitz in a ball $B(p,R)$ with constant $L= L(|\nabla_pf|, R)$.
May 29, 2020 at 2:25 comment added ccriscitiello Thanks for your response. How do we know the sequence of functions $\phi_n$ has a pointwise convergent subsequence?
Apr 22, 2020 at 2:15 history undeleted Anton Petrunin
Apr 22, 2020 at 2:15 history edited Anton Petrunin CC BY-SA 4.0
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Apr 22, 2020 at 2:03 history edited Anton Petrunin CC BY-SA 4.0
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Apr 22, 2020 at 2:01 history deleted Anton Petrunin via Vote
Apr 22, 2020 at 1:43 history answered Anton Petrunin CC BY-SA 4.0