| Title |
The Neumann problem on ellipsoids
|
|---|---|
| Published in |
Journal of Applied Mathematics and Computing, April 2017
|
| DOI | 10.1007/s12190-017-1105-4 |
| Pubmed ID | |
| Authors |
Sheldon Axler, Peter J. Shin |
| Abstract |
The Neumann problem on an ellipsoid in R n asks for a function harmonic inside the ellipsoid whose normal derivative is some specified function on the ellipsoid. We solve this problem when the specified function on the ellipsoid is a normalized polynomial (a polynomial divided by the norm of the normal vector arising from the definition of the ellipsoid). Specifically, we give a necessary and sufficient condition for a solution to exist, and we show that if a solution exists then it is a polynomial whose degree is at most the degree of the polynomial giving the specified function. Furthermore, we give an algorithm for computing this solution. We also solve the corresponding generalized Neumann problem and give an algorithm for computing its solution. |
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Geographical breakdown
| Country | Count | As % |
|---|---|---|
| United States | 1 | 100% |
Demographic breakdown
| Type | Count | As % |
|---|---|---|
| Members of the public | 1 | 100% |
Mendeley readers
The data shown below were compiled from readership statistics for 2 Mendeley readers of this research output. Click here to see the associated Mendeley record.
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Unknown | 2 | 100% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Student > Ph. D. Student | 1 | 50% |
| Student > Master | 1 | 50% |
| Readers by discipline | Count | As % |
|---|---|---|
| Physics and Astronomy | 2 | 100% |
Attention Score in Context
This research output has an Altmetric Attention Score of 1. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 29 April 2017.
All research outputs
#15,457,417
of 22,968,808 outputs
Outputs from Journal of Applied Mathematics and Computing
#14
of 39 outputs
Outputs of similar age
#193,689
of 309,813 outputs
Outputs of similar age from Journal of Applied Mathematics and Computing
#1
of 3 outputs
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