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Title: Fundamental Solution of Laplace’s Equation
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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 3 | Fundamental Solution of Laplace’s Equation
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Forum: Ask a question in Mattermost
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Quiz: Test your knowledge
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Exercise Download PDF sheets
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Subtitle on GitHub: pde03_sub_eng.srt missing
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Timestamps (n/a)
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Subtitle in English (n/a)
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Quiz Content
Q1: What is correct for the Newtonian kernel $\gamma$ in $\mathbb{R}^3$ as we have defined it here?
A1: $\gamma(x) = \frac{1}{\| {x} \|} $
A2: $\gamma(x) = \frac{1}{2 \pi} \log{\| {x} \|} $
A3: $\gamma$ has only negative values.
A4: $\gamma(x)$ goes to infinity when $\|x \|$ tends to zero.
Q2: What is the correct for the Newtonian kernel $\gamma$ in $\mathbb{R}^3$ as we have defined it here?
A1:
$$ \int_{B_1(0)} \gamma(x) \, d^n x = 1 $$A2:
$$ \int_{B_1(0)} \gamma(x) \, d^n x = \frac{1}{4} $$A3:
$$ \int_{B_1(0)} \gamma(x) \, d^n x = 0 $$A4:
$$ \int_{B_1(0)} \gamma(x) \, d^n x = \frac{1}{2} $$ -
Date of video: 2025-09-09
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Last update: 2025-09
