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Akira
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I'm learning Functional Analysis and Probability Theory.

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10
Upper bound Hölder norm of the solution to the non-linear PDE $\partial_t u (t, x) = \Delta_x \{ |\sigma (u (t, x))|^2 u(t, x) \}$
Jan 19
question
7
How is the Gronwall lemma used in this paper?
Feb 23, 2023
question
6
Can Theorem 1.40 in Rudin's Real and Complex Analysis be strengthened when the $\sigma$-algebra is Borel?
Dec 29, 2022
question
5
Is there a Borel measurable $f:\mathbb{R}^d \to \mathbb{R}^d$ such that $f(x) \in \partial \varphi (x)$ for all $x$?
Sep 3, 2023
answer
4
Solution of SDE at finite time, continuity of pdf
Feb 29
question
4
Hausdorff dimension of the non-differentiability set a convex function
Jun 30, 2022
question
4
Hölder stability of the PDE $\partial_t u (t, x) = \operatorname{div} \{ a (t, x) \nabla u(t, x) \}$
Dec 3
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4
Does $f(t) \le \int_0^t (t-s)^{-\frac{1}{2}} [f(s) + |f(s)|^{\beta}] \, \mathrm d s$ imply $f=0$?
Mar 26
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4
Optimal Transport: how is this transport map Borel measurable?
Dec 20, 2022
question
4
Weak uniqueness of an SDE with locally Lipschitz drift and additive noise?
Jan 1
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FutureWarning: The default value of regex will change from True to False in a future version
36
Alternatives to LaTeX
19
Prove that $\lim_{n \rightarrow \infty} \sum_{k=0}^{n} \frac{1}{k!} = e$
14
A detailed and self-contained proof of Tonelli's theorem
11
Julius König's proof of Schröder–Bernstein theorem