Finite distortion functions and Douglas-Dirichlet functionals

Qingtian Shi

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 1, page 183-195
  • ISSN: 0011-4642

Abstract

top
In this paper, we estimate the Douglas-Dirichlet functionals of harmonic mappings, namely Euclidean harmonic mapping and flat harmonic mapping, by using the extremal dilatation of finite distortion functions with given boundary value on the unit circle. In addition, ∂ ¯ -Dirichlet functionals of harmonic mappings are also investigated.

How to cite

top

Shi, Qingtian. "Finite distortion functions and Douglas-Dirichlet functionals." Czechoslovak Mathematical Journal 69.1 (2019): 183-195. <http://eudml.org/doc/294460>.

@article{Shi2019,
abstract = {In this paper, we estimate the Douglas-Dirichlet functionals of harmonic mappings, namely Euclidean harmonic mapping and flat harmonic mapping, by using the extremal dilatation of finite distortion functions with given boundary value on the unit circle. In addition, $\bar\{\partial \}$-Dirichlet functionals of harmonic mappings are also investigated.},
author = {Shi, Qingtian},
journal = {Czechoslovak Mathematical Journal},
keywords = {Douglas-Dirichlet functional; $\rho $-harmonic mapping; finite distortion functions; extremal quasiconformal mapping; Dirichlet’s principle},
language = {eng},
number = {1},
pages = {183-195},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite distortion functions and Douglas-Dirichlet functionals},
url = {http://eudml.org/doc/294460},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Shi, Qingtian
TI - Finite distortion functions and Douglas-Dirichlet functionals
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 183
EP - 195
AB - In this paper, we estimate the Douglas-Dirichlet functionals of harmonic mappings, namely Euclidean harmonic mapping and flat harmonic mapping, by using the extremal dilatation of finite distortion functions with given boundary value on the unit circle. In addition, $\bar{\partial }$-Dirichlet functionals of harmonic mappings are also investigated.
LA - eng
KW - Douglas-Dirichlet functional; $\rho $-harmonic mapping; finite distortion functions; extremal quasiconformal mapping; Dirichlet’s principle
UR - http://eudml.org/doc/294460
ER -

References

top
  1. Astala, K., Iwaniec, T., Martin, G. J., 10.1515/9781400830114, Princeton Mathematical Series 48, Princeton University Press, Princeton (2009). (2009) Zbl1182.30001MR2472875DOI10.1515/9781400830114
  2. Astala, K., Iwaniec, T., Martin, G. J., Onninen, J., 10.1112/S0024611505015376, Proc. Lond. Math. Soc., III. Ser. 91 (2005), 655-702. (2005) Zbl1089.30013MR2180459DOI10.1112/S0024611505015376
  3. Chen, X., Qian, T., 10.1080/17476933.2014.984292, Complex Var. Elliptic Equ. 60 (2015), 875-892. (2015) Zbl1317.30025MR3345479DOI10.1080/17476933.2014.984292
  4. Duren, P., 10.1017/CBO9780511546600, Cambridge Tracts in Mathematics 156, Cambridge University Press, Cambridge (2004). (2004) Zbl1055.31001MR2048384DOI10.1017/CBO9780511546600
  5. Feng, X., 10.3969/j.issn.1008-5513.2016.02.002, Pure Appl. Math. 32 (2016), 119-126 Chinese. (2016) Zbl1363.30046DOI10.3969/j.issn.1008-5513.2016.02.002
  6. Feng, X., Tang, S., 10.1007/s00013-016-0906-2, Arch. Math. 107 (2016), 81-88. (2016) Zbl1352.30037MR3514730DOI10.1007/s00013-016-0906-2
  7. Hencl, S., Koskela, P., Onninen, J., 10.4310/MRL.2005.v12.n2.a8, Math. Res. Lett. 12 (2005), 231-237. (2005) Zbl1079.30024MR2150879DOI10.4310/MRL.2005.v12.n2.a8
  8. Kalaj, D., Mateljević, M., 10.1007/BF02916757, J. Anal. Math. 100 (2006), 117-132. (2006) Zbl1173.30311MR2303306DOI10.1007/BF02916757
  9. Li, Z., 10.1007/BF02882940, Chin. Sci. Bull. 42 (1997), 2025-2045. (1997) Zbl0905.30017MR1641041DOI10.1007/BF02882940
  10. Mateljević, M., 10.2298/PIM0475147M, Publ. Inst. Math., Nouv. Sér. 75(89) (2004), 147-171. (2004) Zbl1081.30022MR2108004DOI10.2298/PIM0475147M
  11. Mateljević, M., Dirichlet's principle, uniqueness of harmonic maps and extremal QC mappings, Zbornik Radova (Beograd) 10(18) (2004), 41-91. (2004) Zbl1289.30001MR2109104
  12. Qi, Y., Shi, Q., 10.2298/FIL1702335Y, Filomat 31 (2017), 335-345. (2017) MR3628843DOI10.2298/FIL1702335Y
  13. Reich, E., 10.5186/aasfm.1985.1052, Ann. Acad. Sci. Fenn., Ser. A I, Math. 10 (1985), 469-475. (1985) Zbl0592.30027MR0802510DOI10.5186/aasfm.1985.1052
  14. Reich, E., 10.1007/BF02796588, J. Anal. Math. 46 (1986), 239-245. (1986) Zbl0608.30023MR0861702DOI10.1007/BF02796588
  15. Schoen, R., Yau, T. S., 10.1007/BF01403164, Invent. Math. 44 (1978), 265-278. (1978) Zbl0388.58005MR0478219DOI10.1007/BF01403164
  16. Shen, Y., Quasiconformal mappings and harmonic functions, Adv. Math., Beijing 28 (1999), 347-357. (1999) Zbl1054.30506MR1767643
  17. Shen, Y., 10.1006/jmaa.2000.6806, J. Math. Anal. Appl. 247 (2000), 27-44. (2000) Zbl0961.30011MR1766923DOI10.1006/jmaa.2000.6806
  18. Wei, H., 10.1090/S0002-9939-96-03178-4, Proc. Am. Math. Soc. 124 (1996), 2337-2341. (1996) Zbl0858.30014MR1307523DOI10.1090/S0002-9939-96-03178-4
  19. Yao, G., 10.1090/S0002-9939-02-06757-6, Proc. Am. Math. Soc. 131 (2003), 2271-2277. (2003) Zbl1074.30018MR1963777DOI10.1090/S0002-9939-02-06757-6
  20. Yao, G., 10.1002/mana.200310294, Math. Nachr. 278 (2005), 1086-1096. (2005) Zbl1083.30020MR2150380DOI10.1002/mana.200310294

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.