Solvability of a first order system in three-dimensional non-smooth domains

Michal Křížek; Pekka Neittaanmäki

Aplikace matematiky (1985)

  • Volume: 30, Issue: 4, page 307-315
  • ISSN: 0862-7940

Abstract

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A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain Ω ⊂ 𝐑 3 . On the boundary δ Ω , the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.

How to cite

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Křížek, Michal, and Neittaanmäki, Pekka. "Solvability of a first order system in three-dimensional non-smooth domains." Aplikace matematiky 30.4 (1985): 307-315. <http://eudml.org/doc/15409>.

@article{Křížek1985,
abstract = {A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain $\Omega \subset \mathbf \{R\}^3$. On the boundary $\delta \Omega $, the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.},
author = {Křížek, Michal, Neittaanmäki, Pekka},
journal = {Aplikace matematiky},
keywords = {Friedrich’s inequality; boundary value problem; magnetostatics in vacuum; bounded domain with Lipschitz boundary; Trace theorems; Friedrich's inequality; boundary value problem; magnetostatics in vacuum; bounded domain with Lipschitz boundary; Trace theorems},
language = {eng},
number = {4},
pages = {307-315},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solvability of a first order system in three-dimensional non-smooth domains},
url = {http://eudml.org/doc/15409},
volume = {30},
year = {1985},
}

TY - JOUR
AU - Křížek, Michal
AU - Neittaanmäki, Pekka
TI - Solvability of a first order system in three-dimensional non-smooth domains
JO - Aplikace matematiky
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 4
SP - 307
EP - 315
AB - A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain $\Omega \subset \mathbf {R}^3$. On the boundary $\delta \Omega $, the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.
LA - eng
KW - Friedrich’s inequality; boundary value problem; magnetostatics in vacuum; bounded domain with Lipschitz boundary; Trace theorems; Friedrich's inequality; boundary value problem; magnetostatics in vacuum; bounded domain with Lipschitz boundary; Trace theorems
UR - http://eudml.org/doc/15409
ER -

References

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  1. C. Bernardi, Formulation variationnelle mixte des equations de Navier-Stokes en dimension 3, Thýese de 3ème cycle (deuxième partie), Paris VI (1979), 146-176. (1979) 
  2. B. M. Budak S. V. Fomin, Multiple integrals, field theory and series, Mir Publishers, 1975. (1975) MR0349913
  3. E. B. Byhovskiy, Solution of a mixed problem for the system of Maxwell equations in case of ideally conductive boundary, Vestnik Leningrad. Univ. Mat. Meh. Astronom. 12 (1957), 50-66. (1957) MR0098567
  4. M. Crouzeix, Résolution numérique des équations de Stokes stationnaires. Approximation et méthodes iteratives de resolution d'inequations variationnelles et de problèms non lineaires, IRIA, 1974, 139-211. (1974) 
  5. M. Crouzeix A. Y. Le Roux, Ecoulement d'une fluide irrotationnel, Journées Eléments Finis, Univ. de Rennes, 1976, 1 - 8. (1976) 
  6. G. Duvaut J. L. Lions, Inequalities in mechanics and physics, Springer-Verlag, Berlin, 1976. (1976) MR0521262
  7. A. Friedman, Advanced calculus, Reinhart and Winston, Holt, New York, 1971. (1971) Zbl0225.26002MR0352342
  8. K. O. Friedrichs, 10.1002/cpa.3160080408, Comm. Pure Appl. Math. 8 (1955), 551-590. (1955) Zbl0066.07504MR0087763DOI10.1002/cpa.3160080408
  9. V. Girault P. A. Raviart, Finite element approximation of the Navier-Stokes equation, Springer-Verlag, Berlin, Heidelberg, New York, 1979. (1979) MR0548867
  10. M. Křížek P. Neittaanmäki, 10.7146/math.scand.a-12037, Math. Scand. 54 (1984), 17-26. (1984) MR0753060DOI10.7146/math.scand.a-12037
  11. M. Křížek P. Neittaanmäki, Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains, Apl. Mat. 29 (1984), 272 - 285. (1984) MR0754079
  12. E. Moise, Geometrical topology in dimension 2 and 3, Springer-Verlag, Berlin, Heidelberg, New York, 1977. (1977) 
  13. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
  14. J. Nečas I. Hlaváček, Mathematical theory of elastic and elasto-plastic bodies: an introduction, Elsevier, Amsterdam, Oxford, New York, 1981. (1981) MR0600655
  15. P. Neittaanmäki M. Křížek, Conforming FE-method for obtaining the gradient of a solution to the Poisson equation. Efficient Solvers for Elliptic Systems, (Ed. W. Hackbush), Numerical Methods in Fluid Mechanics, Vieweg, 1984, 73-86. (1984) MR0804088
  16. P. Neittaanmäki J. Saranen, 10.1080/01630568008816072, Numer. Funct. Anal. Optim. 2 (1981), 487-506. (1981) MR0605756DOI10.1080/01630568008816072
  17. Neittaanmaki J. Saranen, 10.1016/0771-050X(82)90038-9, J. Comput. Appl. Math. 8 (1982), 165-169. (1982) DOI10.1016/0771-050X(82)90038-9
  18. R. Picard, 10.1002/mma.1670030116, Math. Methods Appl. Sci. 3 (1981), 218-228. (1981) Zbl0466.31016MR0657293DOI10.1002/mma.1670030116
  19. R. Picard, On the boundary value problems of electro- and magnetostatics, SFB 72, preprint 442 (1981), Bonn. (1981) MR0667134
  20. R. Picard, An elementary proof for a compact imbedding result in the generalized electromagnetic theory, SFB 72, preprint 624 (1984), Bonn. (1984) MR0753428
  21. J. Saranen, 10.1016/0022-247X(82)90179-2, J. Math. Anal. Appl. 88 (1982), 104-115. (1982) Zbl0508.35024MR0661405DOI10.1016/0022-247X(82)90179-2
  22. J. Saranen, 10.1016/0022-247X(83)90104-X, J. Math. Anal. Appl. 91 (1983), 254-275. (1983) MR0688544DOI10.1016/0022-247X(83)90104-X
  23. R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam 1977. (1977) Zbl0383.35057MR0609732
  24. Ch. Weber, 10.1002/mma.1670020103, Math. Methods Appl. Sci. 2 (1980), 12-25. (1980) Zbl0432.35032MR0561375DOI10.1002/mma.1670020103

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