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The uniqueness theorem for Poisson's equation states that, for a large class of boundary conditions, the equation may have many solutions, but the gradient of every solution is the same. In the case of electrostatics, this means that there is a unique electric field derived from a potential function satisfying Poisson's equation under the boundary conditions.

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  • نظرية الفردية لمعادلة بواسون هي نظرية تنص على أن المعادلة لها تدرج واحد فريد في مسائل القيم الحدية , وفي حالة الكهروستاتيكا إذا وجد حقل كهربائي يحقق الشروط الحدية , يكون هذا الحقل هو الحقل الكهربائي الكامل . (ar)
  • The uniqueness theorem for Poisson's equation states that, for a large class of boundary conditions, the equation may have many solutions, but the gradient of every solution is the same. In the case of electrostatics, this means that there is a unique electric field derived from a potential function satisfying Poisson's equation under the boundary conditions. (en)
  • 唯一性定理指出,很大一部分的具有边界条件的泊松方程,可能有很多个解,但所有解的梯度都是相同的。在静电学的情况下,这意味着在边界条件下的泊松方程所解得的势函数具有唯一确定的电场。 (zh)
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  • نظرية الفردية لمعادلة بواسون هي نظرية تنص على أن المعادلة لها تدرج واحد فريد في مسائل القيم الحدية , وفي حالة الكهروستاتيكا إذا وجد حقل كهربائي يحقق الشروط الحدية , يكون هذا الحقل هو الحقل الكهربائي الكامل . (ar)
  • The uniqueness theorem for Poisson's equation states that, for a large class of boundary conditions, the equation may have many solutions, but the gradient of every solution is the same. In the case of electrostatics, this means that there is a unique electric field derived from a potential function satisfying Poisson's equation under the boundary conditions. (en)
  • 唯一性定理指出,很大一部分的具有边界条件的泊松方程,可能有很多个解,但所有解的梯度都是相同的。在静电学的情况下,这意味着在边界条件下的泊松方程所解得的势函数具有唯一确定的电场。 (zh)
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  • مبرهنة الفردية (ar)
  • Uniqueness theorem for Poisson's equation (en)
  • 唯一性定理 (泊松方程) (zh)
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