INFINITESIMAL DEFORMATIONS OF HARMONIC MAPS AND MORPHISMS

We survey results on infinitesimal deformations ("Jacobi fields") of harmonic maps, concentrating on (i) when they are integrable, i.e., arise from genuine deformations, and what this tells us, (ii) their relation with harmonic morphisms — maps which preserve Laplace's equation.

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Stability analysis of the method of fundamental solutions with smooth closed pseudo-boundaries for Laplace’s equation: better pseudo-boundaries

Numerical Algorithms ◽

10.1007/s11075-021-01150-5 ◽

2021 ◽

Author(s):

Li-Ping Zhang ◽

Zi-Cai Li ◽

Ming-Gong Lee ◽

Hung-Tsai Huang

Keyword(s):

Stability Analysis ◽

Fundamental Solutions ◽

Method Of Fundamental Solutions ◽

Laplace’S Equation ◽

Laplace's Equation

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Harmonic maps and harmonic morphisms

Journal of Mathematical Sciences ◽

10.1007/bf02364883 ◽

1999 ◽

Vol 94 (2) ◽

pp. 1263-1269 ◽

Cited By ~ 3

Author(s):

J. C. Wood

Keyword(s):

Harmonic Maps ◽

Harmonic Morphisms

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A CHARACTERIZATION OF JACOBI FIELDS ALONG HARMONIC MAPS

International Journal of Mathematics ◽

10.1142/s0129167x93000297 ◽

1993 ◽

Vol 04 (04) ◽

pp. 545-550 ◽

Cited By ~ 1

Author(s):

MARIA J. FERREIRA

Keyword(s):

Harmonic Maps ◽

Jacobi Fields

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Central difference regularization method for the Cauchy problem of the Laplace’s equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.01.056 ◽

2006 ◽

Vol 181 (1) ◽

pp. 675-684 ◽

Cited By ~ 22

Author(s):

Xiang-Tuan Xiong ◽

Chu-Li Fu

Keyword(s):

Cauchy Problem ◽

Regularization Method ◽

Laplace’S Equation ◽

Central Difference ◽

Laplace's Equation ◽

The Cauchy Problem

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Approximate analytic solution of the Dirichlet problems for Laplace’s equation in planar domains by a perturbation method

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2011.10.072 ◽

2012 ◽

Vol 63 (1) ◽

pp. 60-67 ◽

Cited By ~ 2

Author(s):

E. Di Costanzo ◽

A. Marasco

Keyword(s):

Perturbation Method ◽

Analytic Solution ◽

Approximate Analytic Solution ◽

Laplace’S Equation ◽

Dirichlet Problems ◽

Laplace's Equation ◽

Planar Domains

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An efficient finite element method for treating singularities in Laplace's equation

Journal of Computational Physics ◽

10.1016/0021-9991(91)90242-d ◽

1991 ◽

Vol 96 (2) ◽

pp. 391-410 ◽

Cited By ~ 35

Author(s):

Lorraine G Olson ◽

Georgios C Georgiou ◽

William W Schultz

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Laplace’S Equation ◽

Laplace's Equation ◽

Element Method

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A note on the estimation of the optimum successive overrelaxation parameter for Laplace's equation

The Computer Journal ◽

10.1093/comjnl/10.4.400 ◽

1968 ◽

Vol 10 (4) ◽

pp. 400-401 ◽

Cited By ~ 6

Author(s):

T. J. Randall

Keyword(s):

Laplace’S Equation ◽

Successive Overrelaxation ◽

Laplace's Equation

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Note on the electric capacity coefficients of spheres

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1912.0101 ◽

1912 ◽

Vol 87 (598) ◽

pp. 485-487

Keyword(s):

General Solution ◽

Laplace’S Equation ◽

Laplace's Equation ◽

Electric Capacity ◽

Physical Problems

In the 'Proceedings' of the Society, vol. 87, p. 109, Mr. Jeffery obtains a general solution of Laplace’s equation in a form suitable for physical problems in connection with two spheres. As an illustration he applies his solution to the problem of finding the capacity coefficients of two equal spheres, obtaining a result which he shows to be equivalent to one of Maxwell’s series formulæ. He then computes a table of the numerical values of these coefficients.

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