| Title:
|
Martin boundary associated with a system of PDE (English) |
| Author:
|
Benyaiche, Allami |
| Author:
|
Ghiate, Salma |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
399-425 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study the Martin boundary associated with a harmonic structure given by a coupled partial differential equations system. We give an integral representation for non negative harmonic functions of this structure. In particular, we obtain such results for biharmonic functions (i.e. $\triangle^{2}\varphi =0$) and for non negative solutions of the equation $\triangle^{2}\varphi =\varphi $. (English) |
| Keyword:
|
Martin boundary |
| Keyword:
|
biharmonic functions |
| Keyword:
|
coupled partial differential equations |
| MSC:
|
31B10 |
| MSC:
|
31B30 |
| MSC:
|
31C35 |
| MSC:
|
35C15 |
| MSC:
|
35J40 |
| MSC:
|
60J50 |
| idZBL:
|
Zbl 1132.31005 |
| idMR:
|
MR2281003 |
| . |
| Date available:
|
2009-05-05T16:58:13Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119602 |
| . |
| Reference:
|
[1] Benyaiche A.: On almost biharmonic functions in $\Bbb R^n$.Publ. Math., Ec. Norm. Supér, Takaddoum 4 (1988), 47-53 (See Zbl. Math. 678). |
| Reference:
|
[2] Benyaiche A.: Distributions bi-sousharmoniques sur $\Bbb R^n$ $(n \geq 2)$.Math. Bohem. 119 (1994), 1 1-13. MR 1303547 |
| Reference:
|
[3] Benyaiche A.: Mesures de représentation sur les espaces biharmoniques.Proc. ICPT 91, Kluwer Acad. Publ., Dordrecht, 1994, pp.171-178. Zbl 0824.31006, MR 1293761 |
| Reference:
|
[4] Benyaiche A., Ghiate S.: Propriété de moyenne restriente associée à un système d'E.D.P..Rend. Accad. Naz. Sci. XL Mem. Mat. Appl. (1) 27 (2003), 125-143. MR 2056415 |
| Reference:
|
[5] Benyaiche A., Ghiate S.: Frontière de Martin biharmonique.preprint, 2000. |
| Reference:
|
[6] Benyaiche A., El Gourari A.: Caractérisation des ensembles essentiels.J. Math. Soc. Japan 54 2 (2002), 467-486. MR 1883527 |
| Reference:
|
[7] Bliedtner J., Hansen W.: Potential Theory: An Analytic and Probabilistic Approach to Balayage.Universitext, Springer, Berlin, 1986. Zbl 0706.31001, MR 0850715 |
| Reference:
|
[8] Boukricha A.: Espaces biharmoniques.Théorie du potentiel (Orsay, 1983), Lecture Notes in Math. 1096, Springer, Berlin, 1984, pp.116-149. Zbl 0567.31006, MR 0890356 |
| Reference:
|
[9] Bouleau N.: Espaces biharmoniques et couplage de processus de Markov.J. Math. Pures Appl. 59 (1980), 187-240. Zbl 0403.60068, MR 0581988 |
| Reference:
|
[10] Brelot M.: On Topologies and Boundaries in Potential Theory.Lecture Notes in Math. 175, Springer, Berlin, 1971. Zbl 0277.31002, MR 0281940 |
| Reference:
|
[11] Brelot M.: Eléments de la théorie classique du potentiel.4ème edition, Centre de Documentation Universitaire, Paris, 1969. Zbl 0116.07503, MR 0106366 |
| Reference:
|
[12] Constantinescu C., Cornea A.: Potential Theory on Harmonic Spaces.Springer, New York-Heidelberg, 1972. Zbl 0248.31011, MR 0419799 |
| Reference:
|
[13] Doob J.L.: Classical Potential Theory and its Probabilistic Counterpart.Springer, New York, 1984. Zbl 0990.31001, MR 0731258 |
| Reference:
|
[14] Hansen W.: Modification of balayage spaces by transitions with application to coupling of PDE's.Nagoya Math. J. 169 (2003), 77-118. Zbl 1094.31005, MR 1962524 |
| Reference:
|
[15] Helms L.L.: Introduction to Potential Theory.Wiley, New York, 1969. Zbl 0188.17203, MR 0261018 |
| Reference:
|
[16] Phelps R.R.: Lectures on Choquet's Theorem.Van Nostrand, Princeton-Toronto-London, 1966. Zbl 0997.46005, MR 0193470 |
| Reference:
|
[17] Hervé R.M.: Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel.Ann. Inst. Fourier 12 (1962), 415-571. MR 0139756 |
| Reference:
|
[18] Hervé R.M., Hervé M.: Les fonctions surharmoniques associées à un opérateur elliptique du second ordre à coefficients discontinus.Ann. Inst. Fourier 19 1 (1969), 305-359. MR 0261027 |
| Reference:
|
[19] Meyer M.: Balayage spaces on topological sums.Potential Theory (Prague, 1987), Plenum, New York, 1988, pp. 237-246. Zbl 0691.31004, MR 0986301 |
| Reference:
|
[20] Nakai M.: Martin boundary over an isolated singularity of rotation free density.J. Math. Soc. Japan 26 (1974), 483-507. Zbl 0281.30012, MR 0361119 |
| Reference:
|
[21] Smyrnelis E.P.: Axiomatique des fonctions biharmoniques, I.Ann. Inst. Fourier 26 1 35-97 (1976). MR 0477101 |
| Reference:
|
[22] Smyrnelis E.P.: Axiomatique des fonctions biharmoniques, II.Ann. Inst. Fourier 26 3 1-47 (1976). MR 0477101 |
| . |
