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Title: Uniqueness of the Boundary Value Problem for Poisson’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 7 | Uniqueness of the Boundary Value Problem for Poisson’s Equation
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Subtitle on GitHub: pde07_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: Let $f \in C(\Omega)$. What is Poisson’s equation?
A1: $\Delta u = f$
A2: $\Delta u = 0$
A3: $\Delta f = 0$
A4: $\Delta (f-u) = 0$
Q2: Let’s $u$ be solution of Poisson’s equation $\Delta u = f$ on a domain $\Omega$. What do we need when we say that $u$ satisfies the Dirichlet boundary condition with respect to a function $g \in C(\partial\Omega)$?
A1: $u|_{\partial\Omega} = g$
A2: $u|_{\Omega} = g$
A3: There is a $x \in \partial \Omega$ with $u(x) = g(x)$.
A4: For every $x \in \partial \Omega$ we have $g(x) = 0$.
Q3: Consider an open and bounded set $\Omega$ and the Poisson’s equation $\Delta u = f$ together with the Dirichlet boundary condition $u|_{\partial\Omega} = g$. What can we already say?
A1: There is at most one solution $u$.
A2: There is at no solution $u$.
A3: There is at least one solution $u$.
A4: If $u_1$ and $u_2$ are two solutions, then $u_1 + u_2$ is also a solution.
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Date of video: 2026-02-06
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Last update: 2026-02
