Thinness and non-tangential limit associated to coupled PDE

Allami Benyaiche; Salma Ghiate

Commentationes Mathematicae Universitatis Carolinae (2013)

  • Volume: 54, Issue: 1, page 41-51
  • ISSN: 0010-2628

Abstract

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In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. ▵ 2 ϕ = 0 ) and equations of ▵ 2 ϕ = ϕ type.

How to cite

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Benyaiche, Allami, and Ghiate, Salma. "Thinness and non-tangential limit associated to coupled PDE." Commentationes Mathematicae Universitatis Carolinae 54.1 (2013): 41-51. <http://eudml.org/doc/252478>.

@article{Benyaiche2013,
abstract = {In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. $\triangle ^\{2\}\varphi = 0$) and equations of $\triangle ^\{2\}\varphi = \varphi $ type.},
author = {Benyaiche, Allami, Ghiate, Salma},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {thinness; non-tangential limit; Martin boundary; biharmonic functions; coupled partial differential equations; thinness; non-tangential limit; Martin boundary; biharmonic function; coupled partial differential equations},
language = {eng},
number = {1},
pages = {41-51},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Thinness and non-tangential limit associated to coupled PDE},
url = {http://eudml.org/doc/252478},
volume = {54},
year = {2013},
}

TY - JOUR
AU - Benyaiche, Allami
AU - Ghiate, Salma
TI - Thinness and non-tangential limit associated to coupled PDE
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2013
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 54
IS - 1
SP - 41
EP - 51
AB - In this paper, we study the reduit, the thinness and the non-tangential limit associated to a harmonic structure given by coupled partial differential equations. In particular, we obtain such results for biharmonic equation (i.e. $\triangle ^{2}\varphi = 0$) and equations of $\triangle ^{2}\varphi = \varphi $ type.
LA - eng
KW - thinness; non-tangential limit; Martin boundary; biharmonic functions; coupled partial differential equations; thinness; non-tangential limit; Martin boundary; biharmonic function; coupled partial differential equations
UR - http://eudml.org/doc/252478
ER -

References

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  2. Benyaiche A., Ghiate S., Frontière de Martin biharmonique, preprint, 2000. 
  3. Benyaiche A., Ghiate S., Propriété de moyenne restreinte associée à un système d'E.D.P., Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (5) 27 (2003), 125–143. MR2056415
  4. Benyaiche A., Ghiate S., Martin boundary associated with a system of PDE, Comment. Math. Univ. Carolin. 47 (2006), no. 3, 399-425. Zbl1132.31005MR2281003
  5. Benyaiche A., On potential theory associated to a coupled PDE, in Complex Analysis and Potential Theory, T.A. Azeroglu and P.M. Tamrazov, eds., Proceedings of the Conference Satellite to ICM 2006, World Sci. Publ., Hackensack, NJ, 2007, pp. 178–186. Zbl1151.31010MR2368350
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  7. Boukricha A., Espaces biharmoniques, in G. Mokobodzki and D. Pinchon, eds., Théorie du Potentiel (Orsay, 1983), pp. 116–149, Lecture Notes in Mathematics, 1096, Springer, Berlin, 1984. Zbl0567.31006MR0890356
  8. Brelot M., On Topologies and Boundaries in Potential Theory, Lecture Notes in Mathematics, 175, Springer, Berlin-New York, 1971. Zbl0277.31002MR0281940
  9. Constantinescu C., Cornea A., Potential Theory on Harmonic Spaces, Springer, New York-Heidelberg, 1972. Zbl0248.31011MR0419799
  10. Doob J.L., Classical Potential Theory and its Probabilistics Conterpart, Springer, New York, 1984. MR0731258
  11. Hansen W., Modification of balayage spaces by transitions with application to coupling of PDE's, Nagoya Math. J. 169 (2003), 77–118. Zbl1094.31005MR1962524
  12. Smyrnélis E.P., 10.5802/aif.544, Ann. Inst. Fourier (Grenoble) 25 (1975), no. 1, 35–98. Zbl0295.31006MR0382691DOI10.5802/aif.544

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