Uniqueness theorem for Poisson's equation

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Proving an important theorem that has applications in electrostatics and Newtonian gravity. The theorem states that solutions to Poisson's equation are unique, possibly up to an additive constant (depending on whether Dirichlet or Neumann boundary conditions are given).

About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.

#physics #mathematics #maths #math #poisson #equation #PDEs #laplacian #operator #vectorcalculus #vectors #calculus #boundaryconditions #dirichlet #neumann #uniqueness #theorem #gradient #divergence #gravity #electromagnetism #electrostatics #science #education

Dr Ben Yelverton

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Love your work! You explained well in this video, thank you so much for uploading this.

黃-xh

You should've mentioned that this is one of several uniqueness theorems (this one is for Dirichlet problem). In particular, in Electrostatics there is another one for the case when the charges on the conductors are fixed . For example, if you place uncharged sphere in the electric field, the theorem you presented is not useful.

xgx

Thank you Dr. for your lecture . My question is is this uniqueness theorem is holds for sobolev space? If it is please one video for the proof of it.

Mathswithali

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