The Properties of the Weighted Space H 2 , α k ( Ω ) and Weighted Set W 2 , α k ( Ω , δ )

V.A. Rukavishnikov; E.V. Matveeva; E.I. Rukavishnikova

Communications in Mathematics (2018)

  • Volume: 26, Issue: 1, page 31-45
  • ISSN: 1804-1388

Abstract

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We study the properties of the weighted space H 2 , α k ( Ω ) and weighted set W 2 , α k ( Ω , δ ) for boundary value problem with singularity.

How to cite

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Rukavishnikov, V.A., Matveeva, E.V., and Rukavishnikova, E.I.. "The Properties of the Weighted Space $H_{2,\alpha }^k(\Omega )$ and Weighted Set $W_{2,\alpha }^k(\Omega ,\delta )$." Communications in Mathematics 26.1 (2018): 31-45. <http://eudml.org/doc/294734>.

@article{Rukavishnikov2018,
abstract = {We study the properties of the weighted space $H_\{2,\alpha \}^k(\Omega )$ and weighted set $W_\{2,\alpha \}^k(\Omega ,\delta )$ for boundary value problem with singularity.},
author = {Rukavishnikov, V.A., Matveeva, E.V., Rukavishnikova, E.I.},
journal = {Communications in Mathematics},
keywords = {weighted functional spaces; weighted functional sets; weighted Sobolev spaces},
language = {eng},
number = {1},
pages = {31-45},
publisher = {University of Ostrava},
title = {The Properties of the Weighted Space $H_\{2,\alpha \}^k(\Omega )$ and Weighted Set $W_\{2,\alpha \}^k(\Omega ,\delta )$},
url = {http://eudml.org/doc/294734},
volume = {26},
year = {2018},
}

TY - JOUR
AU - Rukavishnikov, V.A.
AU - Matveeva, E.V.
AU - Rukavishnikova, E.I.
TI - The Properties of the Weighted Space $H_{2,\alpha }^k(\Omega )$ and Weighted Set $W_{2,\alpha }^k(\Omega ,\delta )$
JO - Communications in Mathematics
PY - 2018
PB - University of Ostrava
VL - 26
IS - 1
SP - 31
EP - 45
AB - We study the properties of the weighted space $H_{2,\alpha }^k(\Omega )$ and weighted set $W_{2,\alpha }^k(\Omega ,\delta )$ for boundary value problem with singularity.
LA - eng
KW - weighted functional spaces; weighted functional sets; weighted Sobolev spaces
UR - http://eudml.org/doc/294734
ER -

References

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  1. Apel, T., Sändig, A-M., Whiteman, J.R., 10.1002/(SICI)1099-1476(19960110)19:1<63::AID-MMA764>3.0.CO;2-S, Math. Methods Appl. Sci., 19, 1, 1996, 63-85, (1996) MR1365264DOI10.1002/(SICI)1099-1476(19960110)19:1<63::AID-MMA764>3.0.CO;2-S
  2. Arroyo, D., Bespalov, A., Heuer, N., 10.1090/S0025-5718-06-01910-7, Math. Comp., 76, 258, 2007, 509-537, (2007) MR2291826DOI10.1090/S0025-5718-06-01910-7
  3. Assous, F., Ciarlet, J., Garcia, E., Segré, J., 10.1016/j.cma.2006.07.007, Comput. Methods Appl. Mech. Engrg., 196, 1--3, 2006, 665-681, (2006) MR2270148DOI10.1016/j.cma.2006.07.007
  4. Assous, F., Jr, P. Ciarlet, Segré, J., 10.1006/jcph.2000.6499, J. Comput. Phys., 161, 1, 2000, 218-249, (2000) MR1762079DOI10.1006/jcph.2000.6499
  5. Belytschko, T., Gracie, R., Ventura, G., 10.1088/0965-0393/17/4/043001, Model. Simul. Sci. Eng., 17, 4, 2009, 043001, (2009) DOI10.1088/0965-0393/17/4/043001
  6. Bordas, S., Duflot, M., Le, P., 10.1002/cnm.1001, Int. J. Numer. Methods Eng., 24, 2008, 961-971, (2008) MR2474664DOI10.1002/cnm.1001
  7. Byfut, A., Schrödinger, A., 10.1002/nme.3293, Int. J. Numer. Methods Eng., 89, 2012, 1392-1418, (2012) MR2899574DOI10.1002/nme.3293
  8. Costabel, M., Dauge, M., 10.1007/s002110100388, Numer. Math., 93, 2, 2002, 239-277, (2002) MR1941397DOI10.1007/s002110100388
  9. Costabel, M., Dauge, M., Schwab, C., 10.1142/S0218202505000480, Math. Models Methods Appl. Sci., 15, 4, 2005, 575-622, (2005) MR2137526DOI10.1142/S0218202505000480
  10. Ivannikov, V., Tiago, C., Almeida, J.P. Moitinho de, Díez, P., Meshless methods in dual analysis: theoretical and implementation issues, Proceedings of the V International Conference on Adaptive Modeling and Simulation (ADMOS 2011), Paris, France, 2011, 291-308, (2011) 
  11. Li, H., Nistor, V., 10.1016/j.cam.2008.05.009, J. Comput. Appl. Math., 224, 1, 2009, 320-338, (2009) MR2474235DOI10.1016/j.cam.2008.05.009
  12. Liu, G.R., Nguyen-Thoi, T., Smoothed finite elements methods, 2010, CRC Press/Taylor & Francis Group, (2010) 
  13. Morin, P., Hochetto, R.H., Siebert, K.G., 10.1137/S0036144502409093, SIAM Rev., 44, 5, 2002, 631-658, (2002) MR1980447DOI10.1137/S0036144502409093
  14. Nguyen-Xuana, H., Liuc, G.R., Bordasd, S., Natarajane, S., Rabczukf, T., 10.1016/j.cma.2012.07.017, Comput. Methods Appl .Mech. Engrg., 253, 2013, 252-273, (2013) MR3002792DOI10.1016/j.cma.2012.07.017
  15. Nguyen-Thoi, T., Vu-Do, H., Rabczuk, T., Nguyen-Xuan, H., 10.1016/j.cma.2010.06.017, Comput. Methods Appl. Mech. Engrg., 199, 2010, 3005-3027, (2010) MR2740774DOI10.1016/j.cma.2010.06.017
  16. Nguyen, V.P., Rabczuk, T., Bordas, S., Dufolt, M., 10.1016/j.matcom.2008.01.003, Math. Comput. Simulation., 79, 2008, 763-813, (2008) MR2477562DOI10.1016/j.matcom.2008.01.003
  17. Rukavishnikov, V.A., On the differential properties of R ν -generalized solution of Dirichlet problem, Dokl. Akad. Nauk., 309, 6, 1989, 1318-1320, (1989) MR1045325
  18. Rukavishnikov, V.A., 10.1134/S1064562414060155, Dokl. Math., 90, 2, 2014, 562-564, (2014) MR3408915DOI10.1134/S1064562414060155
  19. Rukavishnikov, V.A., Mosolapov, A.O., 10.1016/j.jcp.2011.11.031, J. Comput. Phys., 231, 6, 2012, 2438-2448, (2012) MR2881024DOI10.1016/j.jcp.2011.11.031
  20. Rukavishnikov, V.A, Mosolapov, A.O, 10.1134/S1064562413020105, Dokl. Math., 87, 2, 2013, 156-159, (2013) MR2881024DOI10.1134/S1064562413020105
  21. Rukavishnikov, V.A., Nikolaev, S.G., 10.1134/S1064562415040080, Dokl. Math., 92, 1, 2015, 421-423, (2015) MR3443988DOI10.1134/S1064562415040080
  22. Rukavishnikov, V.A., Nikolaev, S.G., 10.1134/S1064562413060215, Dokl. Math., 88, 3, 2013, 705-709, (2013) MR3203317DOI10.1134/S1064562413060215
  23. Rukavishnikov, V., Rukavishnikova, E., On the existence and uniqueness of R ν -generalized solution for Dirichlet problem with singularity on all boundary, Abstr. Appl. Anal. 2014, 2014, 568726, (2014) MR3230527
  24. Rukavishnikov, V.A., Rukavishnikova, E.I., 10.1134/S0012266116050141, Differ. Equ., 52, 5, 2016, 681-685, (2016) MR3541462DOI10.1134/S0012266116050141
  25. Rukavishnikov, V.A., Rukavishnikova, H.I., 10.1016/j.cam.2010.01.020, J. Comput. Appl. Math., 234, 9, 2010, 2870-2882, (2010) MR2652132DOI10.1016/j.cam.2010.01.020
  26. Rukavishnikov, V.A., Rukavishnikova, H.I., 10.1080/01630563.2013.809582, Numer. Funct. Anal. Optim., 34, 12, 2013, 1328-1347, (2013) MR3175621DOI10.1080/01630563.2013.809582
  27. Zienkiewicz, O.C., Taylor, R.L., Zhu, J.Z., The finite element method: its basis and fundamentals. Sixth edition, 2005, Elsevier, (2005) MR3292660

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