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Title: Proof of Maximum Principle
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Series: Partial Differential Equations
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Chapter: Laplace’s Equation
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YouTube-Title: Partial Differential Equations 6 | Proof of Maximum Principle
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Subtitle on GitHub: pde06_sub_eng.srt missing
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Download bright video: Link on Vimeo
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Download dark video: Link on Vimeo
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Related videos:
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: Let $u: \mathbb{R}^n \rightarrow \mathbb{R}$ be continuous with $u(x_0) < 0$ at a given $x_0 \in \mathbb{R}^n$. What is always correct?
A1: There is an open ball $B_{\varepsilon}(x_0)$ on which $u < 0$.
A2: We have $u(x) < 0$ for all $x \in \mathbb{R}^n$.
A3: There is a point $x \in \mathbb{R}^n$ with $u(x) = 0$.
A4: There is a point $x \in \mathbb{R}^n$ with $u(x) > 0$.
Q2: Let $u: \mathbb{R}^n \rightarrow \mathbb{R}$ be continuous with $M \subseteq \mathbb{R}$ be open. What is correct?
A1: $u^{-1}[M]$ is open.
A2: $u[M]$ is open.
A3: $u^{-1}[M]$ is closed.
A4: $u[M]$ is closed.
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Date of video: 2026-01-14
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Last update: 2026-01
