| Revision as of 11:47, 18 December 2011 editQetuth (talk | contribs)Extended confirmed users29,594 editsm more specific stub type + linked maths← Previous edit | Revision as of 08:00, 29 December 2011 edit undo94.197.84.19 (talk) The Beltrami equation characterises quasiconformal mappingsNext edit → | ||
| Line 6: | Line 6: | ||
| for ''w'' a complex distribution of the ] ''z'' in some open set ''U'', with derivatives that are locally ''L''<sup>2</sup>, and where μ is a given complex function in ''L''<sup>∞</sup>(''U'') of norm less than 1, called the '''Beltrami coefficient'''. | for ''w'' a complex distribution of the ] ''z'' in some open set ''U'', with derivatives that are locally ''L''<sup>2</sup>, and where μ is a given complex function in ''L''<sup>∞</sup>(''U'') of norm less than 1, called the '''Beltrami coefficient'''. | ||
| The Beltrami equation characterises ]s. | |||
| ⚫ | ==See also== | ||
| ⚫ | ==See also== | ||
| *] | |||
| *] | *] | ||
| *] | *] | ||
Revision as of 08:00, 29 December 2011
Not to be confused with Laplace–Beltrami equation.In mathematics, the Beltrami equation, named after Eugenio Beltrami, is the partial differential equation
for w a complex distribution of the complex variable z in some open set U, with derivatives that are locally L, and where μ is a given complex function in L(U) of norm less than 1, called the Beltrami coefficient.
The Beltrami equation characterises quasiconformal mappings.
See also
References
- Ahlfors, Lars V. (1966), Lectures on quasiconformal mappings, Van Nostrand
- Beltrami, Eugenio (1867), "Saggio di interpretazione della geometria non euclidea (Essay on the interpretation of noneuclidean geometry)" (PDF), Giornale di Mathematica (in Italian), 6, JFM 01.0275.02 English translation in Stillwell (1996)
- Douady, Adrien; Buff, X. (2000), Le théorème d'intégrabilité des structures presque complexes. , London Math. Soc. Lecture Note Ser., vol. 274, Cambridge Univ. Press, pp. 307–324
- Hubbard, John Hamal (2006), Teichmüller theory and applications to geometry, topology, and dynamics. Vol. 1, Matrix Editions, Ithaca, NY, ISBN 978-0-9715766-2-9, MR 2245223
- Imayoshi, Y.; Taniguchi, M. (1992), An Introduction to Teichmüller spaces, Springer-Verlag, ISBN 0-387-70088-9
- Iwaniec, Tadeusz; Martin, Gaven (2008), The Beltrami equation, Memoirs of the American Mathematical Society, vol. 191, ISBN 978-0-8218-4045-0, MR 2377904
- Morrey, Charles B. (1936), "On the solutions of quasi-linear elliptic partial differential equations.", Bulletin of the American Mathematical Society, 42 (5): 316, doi:10.1090/S0002-9904-1936-06297-X, ISSN 0002-9904, JFM 62.0565.02
- Morrey, Charles B. Jr. (1938), "On the Solutions of Quasi-Linear Elliptic Partial Differential Equations", Transactions of the American Mathematical Society, 43 (1), American Mathematical Society: 126–166, doi:10.2307/1989904, JSTOR 1989904, Zbl 0018.40501
- Papadopoulos, Athanase, ed. (2007), Handbook of Teichmüller theory. Vol. I, IRMA Lectures in Mathematics and Theoretical Physics, 11, European Mathematical Society (EMS), Zürich, doi:10.4171/029, ISBN 978-3-03719-029-6, MR2284826
- Papadopoulos, Athanase, ed. (2009), Handbook of Teichmüller theory. Vol. II, IRMA Lectures in Mathematics and Theoretical Physics, 13, European Mathematical Society (EMS), Zürich, doi:10.4171/055, ISBN 978-3-03719-055-5, MR2524085
- Stillwell, John (1996), Sources of hyperbolic geometry, History of Mathematics, vol. 10, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0529-9, MR 1402697
 | This mathematical analysis–related article is a stub. You can help Misplaced Pages by expanding it. |