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References
[Ba] Bauer H.: Harmonische Räume und ihre Potentialtheorie (Lecture Notes in Mathematics, Vol. 22). Berlin Heidelberg New York: Springer 1966
[BGM] Berger, M., Gauduchon, P. Mazet, E.: Le Spectre d'une Variété Riemanniene (Lecture Notes in Mathematics, Vol. 194). Berlin Heidelberg New York: Springer 1971
[EG] Evans, L.C., Gariepy, R.F.: Wiener's criterion for the heat equation. Arch. Rat. Mech. Anal.78, 293–314 (1982)
[FG] Fabes, E.B., Garofalo, N.: Mean value properties of solutions to parabolic equations with variable coefficients. J. Math. Anal. Appl.121, 305–316 (1987)
[Fe] Federer, H.: Geometric measure theory (Die Grundlehren der, mathematischen Wissenschaften, Vol. 153). Berlin Heidelberg New York: Springer 1969
[F] Folland, G.B: Introduction to partial differential equations. Princeton Univ. Press 1976
[Fr] Friedman, A.: Partial differential equations of parabolic type. New York. Prentice-Hall 1964
[Fu] Fulks, W.: A mean value theorem for the heat equation. Proc. Am. Math. Soc.17, 6–11 (1966)
[GL] Garofalo, N., Lanconelli, E.: Wiener's criterion for parabolic equations with variable coefficients and its consequences, Trans. Am. Math. Soc.307 (to appear) (1988)
[H] Helms, L.L.: Introduction to potential theory. New York: Wiley-Interscience 1969
[K] Kannai, Y.: Off diagonal short time asymptotics for fundamental solutions of diffusion equations. Commun. Partial Differ. Equations2, 781–830 (1977)
[Ku] Kupcov, L.P.: The mean property and the maximum principle for the parabolic equations of second order. Dokl. Akad. Nauk SSSR242, no. 3 (1978); English transl.: Soviet Math. Dokl.19, 1140–1144 (1978)
[L1] Littman, W.: A strong maximum principle for weaklyL-subharmonic functions. J. Math. Mech.8, 761–770 (1959)
[L2] Littman, W.: Generalized subharmonic functions: Monotonic approximations and an improved maximum principle. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser.17, 207–222 (1963)
[M] Moser, J.: A Harnack inequality for parabolic differential equations. Commun. Pure Appl. Math.17, 101–134 (1964)
[P1] Pini, B.: Sulle equazioni a derivate parziali lineari del secondo ordine in due variabili di tipo parabolico. Ann. Mat. Pura e Appl.32, 179–204 (1951)
[P2] Pini, B.: Magioranti e minoranti delle soluzioni delle equazioni paraboliche, Ann. Mat. Pura Appl., IV. Ser.37, 249–264 (1954)
[P3] Pini, B.: Sulla soluzione generalizzata di Wiener per il primo problema di valori al contorno nel caso parabolico. Rend. Semin. Mat. Univ. Padova23, 422–434 (1954)
[W] Watson, N.A.: A theory of temperatures in several variables. Proc. Lond. Math. Soc.26, (3) 385–417 (1973)
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Garofalo, N., Lanconelli, E. Asymptotic behavior of fundamental solutions and potential theory of parabolic operators with variable coefficients. Math. Ann. 283, 211–239 (1989). https://doi.org/10.1007/BF01446432
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DOI: https://doi.org/10.1007/BF01446432