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Keywords:
thinness; non-tangential limit; Martin boundary; biharmonic functions; coupled partial differential equations
Summary:
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.
References:
[1] Armitage D.H., Stephen J.G.: Classical Potential Theory. Springer, London, 2001. MR 1801253 | Zbl 0972.31001
[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. MR 2056415
[4] Benyaiche A., Ghiate S.: Martin boundary associated with a system of PDE. Comment. Math. Univ. Carolin. 47 (2006), no. 3, 399-425. MR 2281003 | Zbl 1132.31005
[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. MR 2368350 | Zbl 1151.31010
[6] Bliedtner J., Hansen W.: Potential Theory. An Analytic and Probabilistic Approach to Balayage. Universitext, Springer, Berlin, 1986. MR 0850715 | Zbl 0706.31001
[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. MR 0890356 | Zbl 0567.31006
[8] Brelot M.: On Topologies and Boundaries in Potential Theory. Lecture Notes in Mathematics, 175, Springer, Berlin-New York, 1971. MR 0281940 | Zbl 0277.31002
[9] Constantinescu C., Cornea A.: Potential Theory on Harmonic Spaces. Springer, New York-Heidelberg, 1972. MR 0419799 | Zbl 0248.31011
[10] Doob J.L.: Classical Potential Theory and its Probabilistics Conterpart. Springer, New York, 1984. MR 0731258
[11] Hansen W.: Modification of balayage spaces by transitions with application to coupling of PDE's. Nagoya Math. J. 169 (2003), 77–118. MR 1962524 | Zbl 1094.31005
[12] Smyrnélis E.P.: Axiomatique des fonctions biharmoniques, I. Ann. Inst. Fourier (Grenoble) 25 (1975), no. 1, 35–98. DOI 10.5802/aif.544 | MR 0382691 | Zbl 0295.31006
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