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GATE 2016 ME (ME3) – Question 13

Engineering Mathematics · Differential Equations: Heat, wave and Laplace equations · 1 mark · Multiple choice

Solutions of Laplace’s equation having continuous second-order partial derivatives are called

  1. biharmonic functions
  2. harmonic functions
  3. conjugate harmonic functions
  4. error functions

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Show answer and explanation

Correct answer: (B) harmonic functions

Explanation

A twice continuously differentiable function satisfying ∇²u=0 is called harmonic. Therefore **harmonic functions, B**, is the defining term. Analyticity and periodicity are different properties and are not the definition supplied by this PDE.