Understanding Laplacian's Theorem: A Comprehensive Guide

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Discussion Overview

The discussion revolves around the existence of a theorem related to the Laplacian, paralleling known theorems for the gradient, curl, and divergence. Participants explore whether a similar theoretical framework can be established for the Laplacian in the context of mathematical physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires if a theorem exists for the Laplacian analogous to the gradient, curl, and divergence theorems.
  • Another participant suggests using Gauß-Ostrogradski's formula to derive Green's formulas, which are relevant in light diffraction theory.
  • A participant expresses confusion about the identities related to Green's formulas and their applications.
  • Multiple participants question the difficulty of finding information on Wikipedia regarding Green's identities.

Areas of Agreement / Disagreement

The discussion remains unresolved, with no consensus on the existence of a Laplacian theorem or clarity on the related identities.

Contextual Notes

Some participants express difficulty in understanding the mathematical identities discussed, indicating potential gaps in foundational knowledge or assumptions about familiarity with the topic.

Jhenrique
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If exist a theorem for the gradiant, other to the curl(green) and other for the divergence. So, exist a theorem for the laplacian too?
 
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I don't understand what you expect. You can use Gauß-Ostrogradski's formula to generate the so-called Green formulas, which are useful in scalar and vector light diffraction theory (Kirchhoff's formula). Search these items on Wikipedia.
 
I want says that if exist the gradient theorem:
ca8b2c89c9693e534bf73ab7c65d411f.png

the curl theorem:
69a456d0e41ae9b609f7437fa0c73f79.png

and the divergence theorem:
7305fb779e0e3926dfe7ef2d4e93a436.png


So, is possible to define a theorem for the laplacian too?
 

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