Uniform approximation by harmonic polynomials for solving the Dirichlet problem of Laplace’s equation on a disk
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DOI: 10.1007/s10986-025-09673-3
Abstract: In this paper, we study the Dirichlet problem for Laplace’s equation in an open disk. The uniqueness of solutions is ensured by the well-known weak maximum principle. We introduce a novel approach to demonstrate the… read more here.
Keywords: laplace equation; problem laplace; disk; harmonic polynomials ... See more keywords
A New Lower Bound for the Maximal Valence of Harmonic Polynomials
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DOI: 10.1007/s40315-016-0175-x
Abstract: We find a new lower bound for the maximal number of zeros of harmonic polynomials, $$p(z)+\overline{q(z)}$$p(z)+q(z)¯, when $$\deg p = n$$degp=n and $$\deg q = n-2$$degq=n-2. read more here.
Keywords: harmonic polynomials; bound maximal; new lower; lower bound ... See more keywords