Abstract
Let u(x1 x2,..., x n ) be a twice continuously differentiable function defined in a domain D in n-dimensional Euclidean space. The Laplace operator or Laplacian Δ is defined as
. If the equation Δu = 0 is satisfied at each point of a domain D, we say that u is harmonic in D or, simply, that u is a harmonic function.
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© 1984 Springer-Verlag New York, Inc.
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Protter, M.H., Weinberger, H.F. (1984). Elliptic Equations. In: Maximum Principles in Differential Equations. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5282-5_2
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DOI: https://doi.org/10.1007/978-1-4612-5282-5_2
Publisher Name: Springer, New York, NY
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