journal article May 01, 1983

Stability of classes of multidimensional holomorphic mappings. III. Properties of mappings that are close to holomorphic mappings

View at Publisher Save 10.1007/bf00971549
Topics

No keywords indexed for this article. Browse by subject →

References
28
[1]
A. P. Kopylov, “On the stability of classes of multidimensional holomorphic mappings. I. The concept of stability. Liouville's theorem,” Sib. Mat. Zh.,23, No. 2, 83–111 (1982). 10.1007/bf00971693
[2]
A. P. Kopylov, “On the stability of classes of multidimensional holomorphic mappings. II. The stability of classes of holomorphic mappings,” Sib. Mat. Zh.,23, No. 4, 65–89 (1982). 10.1007/bf00968655
[3]
B. V. Boyarskii, “Homeomorphic solutions of Beltrami systems,” Dokl. Akad. Nauk SSSR,102, No. 5, 661–664 (1955).
[4]
O. Lehto, “Remarks on the integrability of the derivatives of quasiconformal mappings,” Ann. Acad. Sci. Fenn. Ser. A, I,371, 1–8 (1965).
[5]
Yu. G. Reshetnyak, “Stability estimates in Liouville's theorem, and the Lp-integrability of the derivatives of quasiconformal mappings” Sib. Mat. Zh.,17, No. 4, 868–896 (1976).
[6]
Yu. G. Reshetnyak, “Stability estimates in the class Wp in Liouville's conformal mapping theorem for a closed domain,” Sib. Mat. Zh.,17, No. 6, 1382–1394 (1976).
[7]
A. P. Calderon and A. Zygmund, “On the existence of certain singular integrals,” Acta Math.,88, 85–139 (1952). 10.1007/bf02392130
[8]
S. P. Ponomarev, “On a certain quasiconformality criterion,” Mat. Zametki,9, No. 6, 663–666 (1971).
[9]
S. L. Sobolev, Applications of Functional Analysis in Mathematical Physics, Amer. Math. Soc., Providence (1963). 10.1090/mmono/007
[10]
B. A. Fuks, Special Chapters in the Theory of Analytic Functions of Several Complex Variables [in Russian], Fizmatgiz, Moscow (1963).
[11]
B. V. Boyarskii, “A general representation of the solutions of an elliptic system of 2n equations in a plane,” Dokl. Akad. Nauk SSSR,122, No. 4, 543–546 (1958).
[12]
B. V. Boyarskii, “Theory of generalized analytic vectors,” Ann. Polon. Math.,17, 281–320 (1966). 10.4064/ap-17-3-281-320
[13]
A. Douglis, “A function-theoretic approach to elliptic systems of equations in two variables,” Commun. Pure Appl. Math.,6, No. 2, 259–289 (1953). 10.1002/cpa.3160060205
[14]
A. V. Abrosimov, “The Beltrami system with several independent complex variables,” Dokl. Akad. Nauk SSSR,236, No. 6, 1289–1292 (1977).
[15]
I. N. Vekua, Generalized Analytic Functions, Pergamon (1962).
[16]
P. P. Belinskii, “Stability in Kiouville's theorem on spatial quasiconformal mappings,” in: Certain Problems of Mathematics and Mechanics [in Russian], Nauka, Leningrad (1970). pp. 88–102.
[17]
Yu. G. Reshetnyak, “Stability in Liouville's theorem on conformal mappings of a space for domains with a nonsmooth boundary,” Sib. Mat. Zh.,17, No. 2, 361–369 (1976).
[18]
F. John, “Rotation and strain,” Commun. Pure Appl. Math.,14, No. 3, 381–413 (1961). 10.1002/cpa.3160140315
[19]
L. G. Gurov, “On the stability of Lorentz mappings,” Dokl. Akad. Nauk SSSR,213, No. 2, 267–269 (1973).
[20]
L. G. Gurov, “Stability estimates of Lorentz mappings,” Sib. Mat. Zh.,15, No. 3, 498–515 (1974). 10.1007/bf00969804
[21]
L. G. Gurov, “On the stability of Lorentz transformations. Estimates for the derivatives,” Dokl. Akad. Nauk SSSR,220, No. 2, 273–276 (1975).
[22]
L. G. Gurov, “On the stability of Lorentz transformations in the space,” Sib. Mat. Zh.,21, No. 2, 51–60 (1980). 10.1007/bf00968265
[23]
On functions of bounded mean oscillation

F. John, L. Nirenberg

Communications on Pure and Applied Mathematics 1961 10.1002/cpa.3160140317
[24]
L. G. Gurov and Yu. G. Reshetnyak, “On a certain analogue of the concept of a function with bounded mean oscillation,” Sib. Mat. Zh.,17, No. 3, 540–546 (1976). 10.1007/bf00967861
[25]
L. Ahlfors, Lectures on Quasiconformal Mappings, Van Nostrand, Princeton (1966).
[26]
P. P. Belinskii, “On normality of families of quasiconformal mappings,” Dokl. Akad. Nauk SSSR,128, No. 4, 651–652 (1959).
[27]
F. W. Gehring, “Rings and quasiconformal mappings in space,” Trans. Amer. Math. Soc.,103, No. 3, 353–393 (1962). 10.1090/s0002-9947-1962-0139735-8
[28]
V. M. Gol'dshtein, “The degree of summability of generalized derivatives of plane quasiconformal homeomorphisms,” Dokl. Akad. Nauk SSSR,250, No. 1, 18–21 (1980).
Metrics
1
Citations
28
References
Details
Published
May 01, 1983
Vol/Issue
24(3)
Pages
373-391
License
View
Cite This Article
A. P. Kopylov (1983). Stability of classes of multidimensional holomorphic mappings. III. Properties of mappings that are close to holomorphic mappings. Siberian Mathematical Journal, 24(3), 373-391. https://doi.org/10.1007/bf00971549