Abstract
We give a necessary and sufficient condition of Wiener type for the regularity of boundary points for Poincaré-Dirichlet forms; moreover estimates on the modulus of continuity and on the energy decay of a solution at a regular boundary point are studied.
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References
Biroli M., Marchi S. — Wiener estimates for degenerate elliptic equations — Diff. Int. Eq., 2(1989), 511–523.
Biroli M., Mosco U. — Formes de Dirichlet et estimations structurelles dans les milieux discontinus — Comptes Rendus Acad. Sc. Paris, 315, Sfèr. I (1991), 193–198.
Biroli M., Mosco U. — A Saint-Venant principle for Dirichlet forms on discontinuous media — Preprint Laboratoire d’ Analyse Numerique, Université Paris VI (1993).
Biroli M., Mosco U. — Sobolev inequalities for Dirichlet forms on homogeneous spaces. — “Boundary value problems for partial differential equations” essais for 70 birthday of E. Magenes, ed. C. Baiocchi and J.L. Lions, Masson, Paris, 1993.
Biroli M., Mosco U. — Forthcoming paper
Dal Maso G., Mosco U. — Wiener criteria and energy decay for relaxed Dirichlet problems — Arch. Rat. Mech. An., 95 (1986), 345–387.
Fabes E., Jerison D., Kenig C. — The Wiener test for degenerate elliptic equations — Ann. Inst. Fourier, 3 (1982), 151–183.
Fabes E., Kenig C, Serapioni R. — The local regularity of solutions of degenerate elliptic equations — Comm. in P.D.E., 7 (1982), 77–116.
Fefferman C.L., Phong D. — Subelliptic eigenvalue problems — Conference on Harmonic Analysis, Chicago, W. Beckner etc., Wadsworth, 1981, 590–606.
Fefferman C.L., Sanchez Calle A. — Fundamental solution for second order subelliptic operators — Ann. of Math., 124 (1986), 247–272.
Folland G.B., Stein E.M. — Hardy spaces on homogeneous groups — Princeton University press, Princeton, 1982.
Fukushima M. — Dirichlet forms and Markov processes — North Holland Math. 23, North Holland and Kodansha, Amsterdam, 1980.
Hansen W., Hueber H. — The Dirichlet problem for sublaplacian on nilpotent Lie groups — Geometric criteria for regularity — Mat. Zeit., 276 (1987), 537–547.
Jerison D., Sanchez Calle A. — Subelliptic second order differential operators — Lee. Notes in Math. 1277, Springer Verlag, Berlin-Heidelberg-New York, 1987, 46–77.
Littman W., Stampacchia G., Weinberger H. — Regular points for elliptic equations with discontinuous coefficients — Ann. Sc. Norm. Sup. Pisa, 17 (1963), 45–79.
Lu G. — Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander’s condition — Rev. Iberoamericana, 8 (1992),367–440.
Nagel A., Stein E.M., Weinger S. — Balls and metrics defined by vector fields I: Basic properties — Acta Math., 155 (1985), 103–147.
Negrini P., Scomazzani V. — Wiener criterion for degenerate a class of degenerate elliptic operators — J. Diff. Eq., 66 (1987), 151–164.
Sanchez Calle A. — Fundamental solution and geometry of square of vector fields — Inv. Math., 78 (1984), 143–160.
Sturm K. Th. — Analysis on local Dirichlet spaces — Preprint.
Wiener N. The Dirichlet problem — J. Math. Phys., 3 (1924).
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© 1994 Springer Science+Business Media Dordrecht
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Biroli, M. (1994). The Wiener Test for Poincaré-Dirichlet Forms. In: GowriSankaran, K., Bliedtner, J., Feyel, D., Goldstein, M., Hayman, W.K., Netuka, I. (eds) Classical and Modern Potential Theory and Applications. NATO ASI Series, vol 430. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1138-6_9
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DOI: https://doi.org/10.1007/978-94-011-1138-6_9
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