On solving the plateau problem in parametric form
This paper presents a numerical method for finding the solution of Plateau's problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A nu...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171283000307 |
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| _version_ | 1832545341641064448 |
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| author | Baruch cahlon Alan D. Solomon Louis J. Nachman |
| author_facet | Baruch cahlon Alan D. Solomon Louis J. Nachman |
| author_sort | Baruch cahlon |
| collection | DOAJ |
| description | This paper presents a numerical method for finding the solution of Plateau's problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is proven. A numerical example is given. |
| format | Article |
| id | doaj-art-ee8da0acfc114d8f8eb1d2b09251409c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ee8da0acfc114d8f8eb1d2b09251409c2025-02-03T07:26:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016234136110.1155/S0161171283000307On solving the plateau problem in parametric formBaruch cahlon0Alan D. Solomon1Louis J. Nachman2Department of Mathematical Sciences, Oakland University, Rochester 48063, Michigan, USAMathematics and Statistics Research Division, Computer Science Division, Union Carbide Corporation-Nuclear Division, Oak Ridge 37830, Tennessee, USADepartment of Mathematical Sciences, Oakland University, Rochester 48063, Michigan, USAThis paper presents a numerical method for finding the solution of Plateau's problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is proven. A numerical example is given.http://dx.doi.org/10.1155/S0161171283000307minimal surfacealgorithmparametric formDirichlet's integralharmonic function. |
| spellingShingle | Baruch cahlon Alan D. Solomon Louis J. Nachman On solving the plateau problem in parametric form International Journal of Mathematics and Mathematical Sciences minimal surface algorithm parametric form Dirichlet's integral harmonic function. |
| title | On solving the plateau problem in parametric form |
| title_full | On solving the plateau problem in parametric form |
| title_fullStr | On solving the plateau problem in parametric form |
| title_full_unstemmed | On solving the plateau problem in parametric form |
| title_short | On solving the plateau problem in parametric form |
| title_sort | on solving the plateau problem in parametric form |
| topic | minimal surface algorithm parametric form Dirichlet's integral harmonic function. |
| url | http://dx.doi.org/10.1155/S0161171283000307 |
| work_keys_str_mv | AT baruchcahlon onsolvingtheplateauprobleminparametricform AT alandsolomon onsolvingtheplateauprobleminparametricform AT louisjnachman onsolvingtheplateauprobleminparametricform |