Geodesic
On the base and the essential base in parabolic potential theory
Czechoslovak Mathematical Journal, Tome 40 (1990) no. 1, pp. 87-103

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MR Zbl
DOI : 10.21136/CMJ.1990.102361
Classification : 31C45 
Brzezina, Miroslav. On the base and the essential base in parabolic potential theory. Czechoslovak Mathematical Journal, Tome 40 (1990) no. 1, pp. 87-103. doi: 10.21136/CMJ.1990.102361
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[1] G. Anger: Funktionalanalytische Betrachtungen bei Differentialgleichungen unter Verwendung von Methoden der Potentialtheorie I. Akademie-Verlag, Berlin, 1967. | MR | Zbl

[2] H. Bauer: Harmonische Räume und ihre Potentialtheorie. Lecture Notes in Mathematics 22, Springer-Verlag, Berlin, 1966. | MR | Zbl

[3] U. Bauermann: Balayage-Operatoren in der Potentialtheorie. Math. Ann. 231 (1977), 181-186. | DOI | MR | Zbl

[4] J. Bliedtner W. Hansen: Simplicial cones in potential theory. Invent. Math. 29 (1975), 83-110. | DOI | MR

[5] J. Bliedtner W. Hansen: Potential theory, An Analytic and Probabilistic Approach to Balayage. Springer-Verlag, Berlin, 1986. | MR

[6] M. Brelot: Sur les ensembles effilés. Bull. Sci. Math. 68 (1944), 12-36. | MR | Zbl

[7] M. Brelot: Éléments de la theorie classique du potential. 2e ed. Centre de Documentation Universitaire Paris, 1961. | MR

[8] M. Brzezina: Thinness and essential base for the heat equation. (Thesis in Czech) Charles University, Prague, 1986.

[9] M. Brzezina: Base and essential base in parabolic potential theory. Comm. Math. Univ. Carolinae 27 (1986), 631-632.

[10] C. Constantinescu A. Cornea: Potential theory on harmonic spaces. Springer-Verlag, Berlin, 1972. | MR

[11] E. G. Effros L. J. Kazdan: On the Dirichlet problem for the heat equation. Indiana Univ. Math. J. 20 (1971), 683-693. | DOI | MR

[12] C. L. Evans F. R. Gariepy: Wiener's criterion for the heat equation. Arch. Rational Mech. Anal. 78 (1982), 293-314. | DOI | MR

[13] N. Garofalo E. Lanconelli: Wiener's criterion for parabolic equation with variable coefficient and its consequences. Trans. Amer. Math. Soc. (to appear). | MR

[14] W. Hansen: Fegen und Dünheit mit Anwendungen auf die Laplace- und Wärmeleitungs- gleichungen. Ann. Inst. Fourier (Grenoble) 21 (1971), 79-121. | DOI | MR

[15] W. Hansen: Semi-polar sets are almost negligible. J. reine angew. Math. 314 (1980), 217-220. | MR | Zbl

[16] W. Hansen: Semi-polar sets and quasi-balayage. Math. Ann. 257 (1981), 495-517. | DOI | Zbl

[17] E. Lanconelli: Sul problema di Dirichlet per l'equazione del calore. Ann. Math. Pura ed Appl. 97(1973), 83-113. | DOI | MR

[18] I. Netuka: Thinness and the heat equation. Časopis Pěst. Mat. 99 (1974), 293-299. | MR | Zbl

[19] I. Netuka J. Veselý: Harmonic continuation and removable singularities in the axiomatic potential theory. Math. Ann. 234 (1978), 117-123. | DOI | MR

[20] C. J. Oxtoby: Measure and category. Springer-Verlag, Berlin, 1971. | MR | Zbl

[21] G. I. Petrowsky: Zur ersten Randwertaufgabe der Wärmeleitungsgleichung. Compositio Math. 7 (1935), 383 - 419. | MR | Zbl

[22] B. Pini: Sulla regolarità e irregolarita della frontiera per il primo problema di valori al contorno relativo all'equazione del calore. Ann. Math. Pura ed Appl. 40 (1955), 69-88. | DOI | MR | Zbl

[23] V. Sternberg: Über die Gleichung der Wärmeleitung. Math. Ann. 101 (1929), 394-398. | DOI | MR

[24] L. Stocia: On the thinness of a set at a point. Stud. Cerc. Mat. 38 (1986), 382-391. | MR

[25] K. Uchiyama: A probabilistic proof and applications of Wiener's test for the heat operator. (preprint). | Zbl

[26] A. N. Watson: Thermal capacity. Proc. London Math. Soc. (3) 37 (1978), 342-362. | MR | Zbl

[27] A. N. Watson: Thinness and boundary behaviour of potentials for the heat equation. Mathematika 32 (1985), 90-95. | DOI | MR | Zbl

[28] A. N. Watson: Green's functions, potentials, and the Dirichlet problem for the heat equation. Proc. London Math. Soc. (3) 33 (1976), 251-298. | MR

[29] N. Wiener: The Dirichlet problem. J. Math. Phys. 3 (1924), 127-146. | DOI

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