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Harmonic Functions

  • Marin Marin
  • Andreas Öchsner
Chapter

Abstract

We call a harmonic function on the open set \(\Omega \subset \mathrm{I}\!\mathrm{R}^{n}\), any function u which is twice continuously differentiable on \(\Omega \) and which verifies the equation \(\Delta u(x)=0,\forall x\in \Omega \), where \(\Delta \) is the operator of Laplace
$$\Delta u=\sum \limits _{k=1}^n\frac{\partial ^2 u}{\partial x_k^2}.$$

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTransilvania University of BrasovBrasovRomania
  2. 2.Faculty of Mechanical EngineeringEsslingen University of Applied SciencesEsslingenGermany

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