kaithkolesidou
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Exercise: The measure of the boundary of a level set of a Holder continuous function is positive
-1 votes

I think I figured out the missing keys so I will post the whole argument here as an answer. In case, there are still mistakes, please correct me. We know that $f \in C^{1,\alpha}(M)$ for some $0<\...

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Question on Semigroup theory for evolution equations: Strong continuity of analytic semigroup $e^{-tA}$
0 votes

So, I think that I understood the relation. In order for $(e^{-tA})_{t\ge 0}$ to be a strongly continuous semigroup, the following limit must hold: $\lim_\limits{t \to 0} e^{-tA}x=x, \quad \forall x\...

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Exercise: Initial Value Problem for non-homogeneous wave equation on $\mathbb R^3$
0 votes

Ι 've made a mistake in the above calculation. After substitution we get $u(x,t)=\frac{1}{4\pi} \int_{0}^t \int_{\partial Β(x,t-s)} \frac{1}{t-s} dS(y)ds\;=\;\frac{1}{4\pi} \int_{0}^t \frac{1}{t-s} \...

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