Generalized dimension compression under mappings of exponentially integrable distortion

• Autorzy: Aleksandra Zapadinskaya
• Języki publikacji: EN

Abstrakty

EN

We prove a dimension compression estimate for homeomorphic mappings of exponentially integrable distortion via a modulus of continuity result by D. Herron and P. Koskela [Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259]. The essential sharpness of our estimate is demonstrated by an example.

Słowa kluczowe

EN

Mapping of finite distortion; Exponentially integrable distortion; Generalized Hausdorff measure; Hausdorff dimension

Kategorie tematyczne

• 30C65: Quasiconformal mappings in 𝐑 n , other generalizations

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 2
• Strony: 356-363

Daty

wydano

2011-04-01

online

2011-02-18

Twórcy

autor

Aleksandra Zapadinskaya

• University of Jyväskylä

Bibliografia

• [1] Astala K., Gill J.T., Rohde S., Saksman E., Optimal regularity for planar mappings of finite distortion, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2010, 27(1), 1–19 http://dx.doi.org/10.1016/j.anihpc.2009.01.012
• [2] Astala K., Iwaniec T., Koskela P., Martin G., Mappings of BMO-bounded distortion, Math. Ann., 2000, 317(4), 703–726 http://dx.doi.org/10.1007/PL00004420
• [3] Astala K., Iwaniec T., Martin G., Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane, Princeton Math. Ser., 48, Princeton University Press, Princeton, 2009
• [4] Boyarskiĭ B.V., Homeomorphic solutions of Beltrami systems, Dokl. Akad. Nauk SSSR (N.S.), 1955, 102, 661–664
• [5] David G., Solutions de l’équation de Beltrami avec ‖µ‖∞ = 1, Ann. Acad. Sci. Fenn. Ser. A I Math., 1988, 13(1), 25–70
• [6] Falconer K., Fractal Geometry. Mathematical Foundations and Applications, John Wiley & Sons, Chichester, 1990
• [7] Faraco D., Koskela P., Zhong X., Mappings of finite distortion: the degree of regularity, Adv. Math., 2005, 190(2), 300–318 http://dx.doi.org/10.1016/j.aim.2003.12.009
• [8] Gehring F.W., The L p-integrability of the partial derivatives of a quasiconformal mapping, Acta Math., 1973, 130(1), 265–277 http://dx.doi.org/10.1007/BF02392268
• [9] Herron D.A., Koskela P., Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259
• [10] Koskela P., Zapadinskaya A., Zürcher T., Mappings of finite distortion: generalized Hausdorff dimension distortion, J. Geom. Anal., 2010, 20(3), 690–704 http://dx.doi.org/10.1007/s12220-010-9121-8
• [11] Rajala T., Zapadinskaya A., Zürcher T., Generalized Hausdorff dimension distortion in Euclidean spaces under Sobolev mappings, preprint available at http://arxiv.org/abs/1007.2091

Identyfikatory

DOI

10.2478/s11533-011-0008-0