ISSN 1683-3414 (Print) • ISSN 1814-0807 (Online) | |||
Log in |
Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system’s guidelines Submit manuscript ContactsAddress: Vatutina st. 53, Vladikavkaz,
|
Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.23671/VNC.2015.1.7295 On finite lipschitz Orlicz-Sobolev classes
Salimov R. R.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 1.
Abstract:
It is found a sufficient condition of finite Lipschitz of homeomorphisms of the Orlicz-Sobolev class \(W_{\rm loc}^{1,\varphi}\) under a condition of the Calderon type.
Keywords: finitely Lipschitz mapping, \(p\)-modulus, \(p\)-capacity, Orlicz--Sobolev class, Orlicz space, lower \(Q\)-homeomorphism, mappings of finite distortion
Language: Russian
Download the full text
For citation: Salimov R. R. On finite lipschitz Orlicz-Sobolev classes. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 1, pp.64-77.
DOI 10.23671/VNC.2015.1.7295
+ References
1. Gehring F. W. Lipschitz Mappings and the \(p\)-capacity of Ring in \(n\)-space. Advances in the Theory of Riemann Surfaces (Proc. Conf. Stonybrook, N.Y., 1969), Ann. of Math. Studies, 1971, vol. 66, pp. 175-193. 2. Iwaniec T., Sverak V. On Mappings with Integrable Dilatation. Proc. Amer. Math. Soc., 1993, vol. 118, p. 181-188. 3. Iwaniec T., Martin G. Geometrical Function Theory and Non-Linear Analysis, Oxford, Clarendon Press, 2001. 4. Krasnosel'skij M. A., Rutickij Ja. B. Vypuklye Funkcii i Prostranstva Orlicha, Moskva, Gos. Izd-vo Fiz.-Mat. Lit-ry, 1958 (Russian). 5. Maz'ja V. G. Prostranstva S. L. Soboleva, Leningrad, LGU, 1985, 416 p. (Russian). 6. Afanas'eva E. S., Rjazanov V. I., Salimov R. R. About Mappings in Orlicz-Sobolev Classes on Riemannian Manifolds. Ukrainskii Matematichnij Visnik [Ukrainian Mathematical Bulletin], 2011, vol. 8, no. 3, pp. 319-342 (Russian). 7. Alberico A., Cianchi A. Differentiability Properties of Orlicz-Sobolev Functions. Ark. Mat., 2005, vol. 43, pp. 1-28. 8. Calderon A. P. On the Differentiability of Absolutely Continuous Functions. Riv. Math. Univ. Parma, 1951, vol. 2, pp. 203-213. 9. Cianchi A. A Sharp Embedding Theorem for Orlicz-Sobolev Spaces. Indiana Univ. Math. J., 1996, vol. 45, no. 1, pp. 39-65. 10. Donaldson T. Nonlinear Elliptic Boundary-Value Problems in Orlicz-Sobolev Spaces. J. Diff. Eq., 1971, vol. 10, pp. 507-528. 11. Gossez J. P., Mustonen V. Variational Inequalities in Orlicz-Sobolev Spaces. Nonlinear Anal. Theory Meth. Appl., 1987, vol. 11, pp. 379-392. 12. Hsini M. Existence of Solutions to a Semilinear Elliptic System Through Generalized Orlicz-Sobolev Spaces. J. Partial Differ. Equ., 2010, vol. 23, no. 2, pp. 168-193. 13. Iwaniec T., Koskela P., Onninen J. Mappings of finite distortion: Compactness. Ann. Acad. Sci. Fenn. Ser. A1. Math., 2002, vol. 27, no. 2, pp. 391-417. 14. Kovtonjuk D. A., Rjazanov V. I., Salimov R. R., Sevost'janov E. A. Toward the Theory of Orlicz-Sobolev Classes. St. Petersburg Mathematical Journal [Algebra i Analiz, 2013, vol. 25, no. 6, pp. 50-102], 2014, vol. 25, no. 6, pp. 929-963. 15. Koronel J. D. Continuity and k-th Order Differentiability in Orlicz-Sobolev Spaces: WkLA. Israel J. Math., 1976, vol. 24, no. 2, pp. 119-138. 16. Kauhanen J., Koskela P., Maly J. On Functions with Derivatives in a Lorentz Space. Manuscripta Math., 1999, vol. 10, pp. 87-101. 17. Khruslov E. Ya., Pankratov L. S. Homogenization of the Dirichlet variational problems in Sobolev-Orlicz spaces. Operator Theory and its Applications (Winuipeg, MB, 1998), Providence (R.I.), Amer. Math. Soc., 2000, vol. 25, pp. 345-366. 18. Landes R., Mustonen V. Pseudo-Monotone Mappings in Sobolev-Orlicz Spaces and Nonlinear Boundary Value Problems on Unbounded Domains. J. Math. Anal. Appl., 1982, vol. 88, pp. 25-36. 19. Lappalainen V., Lehtonen A. Embedding of Orlicz-Sobolev Spaces in Holder spaces. Ann. Acad. Sci. Fenn. Ser. A1. Math., 1989, vol. 14, no. 1, pp. 41-46. 20. Onninen J. Differentiability of Monotone Sobolev functions. Real. Anal. Exchange., 2000/2001, vol. 26, no. 2, pp. 761-772. 21. Tuominen H. Characterization of Orlicz-Sobolev Space. Ark. Mat., 2007, vol. 45, no. 1, pp. 123-139. 22. Vuillermot P. A. Holder-Regularity for the Solutions of Strongly Nonlinear Eigenvalue Problems on Orlicz-Sobolev Space. Houston J. Math., 1987, vol. 13, pp. 281-287. 23. Vaisala J. Two New Characterizations for Quasiconformality. Ann. Acad. Sci. Fenn. Ser. A1 Math., 1965, vol. 362, pp. 1-12. 24. Menchoff D. Sur les Differencelles Totales des Fonctions Univalentes. Math. Ann., 1931, vol. 105, pp. 75-85. 25. Gehring F. W., Lehto O. On the Total Differentiability of Functions of a Complex Variable. Ann. Acad. Sci. Fenn. Ser. A1. Math., 1959, vol. 272, pp. 3-8. 26. Lehto O., Virtanen K. Quasiconformal Mappings in the Plane, N.Y., Springer-Verlag, 1973. 27. Martio O., Ryazanov V., Srebro U., Yakubov E. Moduli in Modern Mapping Theory, N.Y. etc., Springer, 2009, 367 p. (Springer Monographs in Mathematics.) 28. Martio O., Rickman S., Vaisala J. Definitions for Quasiregular Mappings. Ann. Acad. Sci. Fenn. Ser. A1. Math., 1969, vol. 448, pp. 1-40. 29. Gol'dshtejn V. M., Reshetnjak Ju. G. Vvedenie v Teoriju Funkcij s Obobshhennymi Proizvodnymi i Kvazikonformnye Otobrazhenija, Novosibirsk, Nauka, 1983 (Russian). 30. Gehring F. W. Quasiconformal Mappings. Complex Analysis and its Applications, Vol. 2, International Atomic Energy Agency, Vienna, 1976, pp. 213-268. 31. Hesse J. A p-extremal Length and \(p\)-capacity Equality. Arc. Mat., 1975, vol. 13, pp. 131-144. 32. Shlyk V. A. On the Equality Between \(p\)-capacity and \(p\)-modulus. Siberian Math. J. [Sibirsk. Mat. Zh, 1993, vol. 34, no. 6, pp. 216-221], 1993, vol. 34, no. 6, pp. 1196-1200. 33. Maz'ya V. Lectures on Isoperimetric and Isocapacitary Inequalities in the Theory of Sobolev Spaces. Contemp. Math., 2003, vol. 338, pp. 307-340. 34. Kruglikov V. I. Capacities of Condensors and Quasiconformal in the Mean Mappings in Space. Mat. Sbornik N. S. [Mathematics of the USSR, Sbornik], 1986, vol. 130, no. 2, pp. 185-206 (Russian). 35. Gehring F. W. Rings and Quasiconformal Mappings in Space. Trans. Amer. Math. Soc., 1962, vol. 103, pp. 353-393. 36. Golberg A. Homeomorphisms with Integrally Restricted Moduli. Complex Analysis and Dynamical Systems IV. Part 1: Function Theory and Optimization, Providence (R. I.), Amer. Math. Soc., 2011, pp. 83-98 (Contemp. Math., 553). 37. Vodop'janov S. K., Uhlov A. D. Superposition Operators in Sobolev Spaces. Russian Mathematics (Izvestiya VUZ. Matematika) [Izv. Vyssh. Uchebn. Zaved. Mat., 2002, no. 10, pp. 11-33], 2002, no. 10, pp. 9-31. 38. Vodop'janov S. K., Uhlov A. D. Operatory superpozicii v prostranstvah Lebega i differenciruemost' kvaziadditivnyh funkcij mnozhestva. Vladikavkazskij Matematicheskij Zh. [Vladikavkaz Mathematical J.], 2002, vol. 4, no. 1, pp. 11-33 (Russian). 39. Vodop'yanov S. K. Description of Composition Operators of Sobolev Spaces. Doklady Math., 2005, vol. 71, no. 1, pp. 5-9. 40. Vodop'yanov S. K. Composition Operators on Sobolev Spaces. Complex Analysis and Dynamical Systems II, 2005, pp. 401-415 (Contemp. Math., 382). 41. Lomako T., Salimov R., Sevost'yanov E. On Equicontinuity of Solutions to the Beltrami Equations. Ann. Univ. Bucharest. Math. Ser., 2010, vol. 59, no. 2, pp. 263-274. 42. Kovtonjuk D. A., Petkov I. V., Rjazanov V. I., Salimov R. R. Boundary Behavior and the Dirichlet Problem for the Beltrami Equations. St. Petersburg Math. J. [Algebra i Analiz, 2013, vol. 25, no. 4, pp. 101-124], 2014, vol. 25, no. 4, pp. 587-603. 43. Ryazanov V., Salimov R., Srebro U., Yakubov E. On Boundary Value Problems for the Beltrami Equations. Contemp. Math., 2013, vol. 591, pp. 211-242. 44. Rjazanov V. I., Sevost'janov E. A. Equicontinuous Classes of Ring Q-Homeomorphisms. Sibirskij Matematicheskij Zhurnal [Siberian Mathematical Journal], 2007, vol. 48, no. 6, pp. 1361-1376 (Russian). 45. Salimov R. R. Absolute Continuity on Lines and the Differentiability of a Generalization of Quasiconformal Mappings. Izvestiya: Mathematics [Izv. Ross. Akad. Nauk. Ser. Mat., 2008, vol. 72, no. 5, pp. 141-148], 2008, vol. 72, no. 5, pp. 977-984. 46. Salimov R. R. Estimation of the Measure of the Image of the Ball. Sibirskij Matematicheskij Zhurnal [Siberian Mathematical Journal], 2012, vol. 53, no. 4, pp. 920-930 (Russian). 47. Salimov R. R. On Finitely Lipschitz Space Mappings. Sibirskie Jelektronnye Matematicheskie Izvestija [Siberian Electronoc Mathematical Reports], 2011, vol. 8, pp. 284-295 (Russian). 48. Salimov R. R. On the Lipschitz Property of a Class of Mappings. Math. Notes [Mat. Zametki, 2013, vol. 94, no. 4, pp. 591-599], 2013, vol. 94, no. 4, pp. 559-566. 49. Salimov R. R. On Ring \(Q\)-Mappings with Respect to Non-Conformal Modulus. Dal'nevost. Mat. Zhurn., 2014, vol. 14, no. 2, pp. 257-269 (Russian). 50. Salimov R. R., Sevost'janov E. A. Theory of Ring Q-Mappings and Geometric Function Theory. Sbornik: Mathematics [Mat. Sbornik, 2010, vol. 201, no. 6, pp. 131-158], 2010, vol. 201, no. 5-6, pp. 909-934. 51. Sevost'janov E. A. On the Theory of the Removal of Singularities for Mappings With an Unbounded Characteristic of Quasiconformality. Izvestiya: Mathematics [Izv. Ross. Akad. Nauk. Ser. Mat., 2010, vol. 74, no. 1, pp. 159-174], 2010, vol. 74, no. 1, pp. 151-165. 52. Sevost'janov E. A.On Space Mappings with Integral Restrictions on the Characteristic. St. Petersburg Math. J. [Algebra i Analiz, 2012, vol. 24, no. 1, pp. 131-156], 2013, vol. 24, no. 1, pp. 99-115. 53. Sevost'janov E. A. On the Branch Points of Mappings with the Unbounded Coefficient of Quasiconformality. Sibirskij Matematicheskij Zhurnal [Siberian Mathematical Journal], 2010, vol. 51, no. 5, pp. 1129-1146 (Russian). 54. Kovtonjuk D. A., Rjazanov V. I. K teorii nizhnih Q-gomeomorfizmov, Ukrainskii Matematichnij Visnik [Ukrainian Mathematical Bulletin], 2008, 5, no. 2, pp. 157-181 (Russian). 55. Ziemer W. P. Extremal Length and p-capacity. The Michigan Math. J., 1969, vol. 16, no. 1, pp. 43-51. 56. Federer G. Geometricheskaja Teorija Mery, M., Nauka, 1987, 760 p. (Russian). 57. Reshetnjak Ju. G. Prostranstvennye Otobrazhenija s Ogranichennym Iskazheniem [Space Mappings with Bounded Distortion], Novosibirsk, Nauka, 1982 (Ruassian). 58. Salimov R. R. Lower Estimates of \(p\)-modulus and Mappings of Sobolev's Class. St. Petersburg Mathematical Journal [Algebra i Analiz, 2014, vol. 26, no. 6, pp. 143-171], 2015, vol. 26, no. 6, pp. 965-984. ← Contents of issue |
| |
|||
© 1999-2023 Þæíûé ìàòåìàòè÷åñêèé èíñòèòóò | |||