Title:
|
On the base and the essential base in parabolic potential theory (English) |
Author:
|
Brzezina, Miroslav |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
40 |
Issue:
|
1 |
Year:
|
1990 |
Pages:
|
87-103 |
. |
Category:
|
math |
. |
MSC:
|
31C45 |
idZBL:
|
Zbl 0712.31001 |
idMR:
|
MR1032362 |
DOI:
|
10.21136/CMJ.1990.102361 |
. |
Date available:
|
2008-06-09T15:31:25Z |
Last updated:
|
2020-07-28 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102361 |
. |
Reference:
|
[1] G. Anger: Funktionalanalytische Betrachtungen bei Differentialgleichungen unter Verwendung von Methoden der Potentialtheorie I.Akademie-Verlag, Berlin, 1967. Zbl 0163.11901, MR 0230916 |
Reference:
|
[2] H. Bauer: Harmonische Räume und ihre Potentialtheorie.Lecture Notes in Mathematics 22, Springer-Verlag, Berlin, 1966. Zbl 0142.38402, MR 0210916 |
Reference:
|
[3] U. Bauermann: Balayage-Operatoren in der Potentialtheorie.Math. Ann. 231 (1977), 181-186. Zbl 0351.31011, MR 0492344, 10.1007/BF01361140 |
Reference:
|
[4] J. Bliedtner W. Hansen: Simplicial cones in potential theory.Invent. Math. 29 (1975), 83-110. MR 0387630, 10.1007/BF01390188 |
Reference:
|
[5] J. Bliedtner W. Hansen: Potential theory, An Analytic and Probabilistic Approach to Balayage.Springer-Verlag, Berlin, 1986. MR 0850715 |
Reference:
|
[6] M. Brelot: Sur les ensembles effilés.Bull. Sci. Math. 68 (1944), 12-36. Zbl 0028.36201, MR 0012364 |
Reference:
|
[7] M. Brelot: Éléments de la theorie classique du potential.2e ed. Centre de Documentation Universitaire Paris, 1961. MR 0106366 |
Reference:
|
[8] M. Brzezina: Thinness and essential base for the heat equation.(Thesis in Czech) Charles University, Prague, 1986. |
Reference:
|
[9] M. Brzezina: Base and essential base in parabolic potential theory.Comm. Math. Univ. Carolinae 27 (1986), 631-632. |
Reference:
|
[10] C. Constantinescu A. Cornea: Potential theory on harmonic spaces.Springer-Verlag, Berlin, 1972. MR 0419799 |
Reference:
|
[11] E. G. Effros L. J. Kazdan: On the Dirichlet problem for the heat equation.Indiana Univ. Math. J. 20 (1971), 683-693. MR 0268543, 10.1512/iumj.1971.20.20054 |
Reference:
|
[12] C. L. Evans F. R. Gariepy: Wiener's criterion for the heat equation.Arch. Rational Mech. Anal. 78 (1982), 293-314. MR 0653544, 10.1007/BF00249583 |
Reference:
|
[13] N. Garofalo E. Lanconelli: Wiener's criterion for parabolic equation with variable coefficient and its consequences.Trans. Amer. Math. Soc. (to appear). MR 0951629 |
Reference:
|
[14] W. Hansen: Fegen und Dünheit mit Anwendungen auf die Laplace- und Wärmeleitungs- gleichungen.Ann. Inst. Fourier (Grenoble) 21 (1971), 79-121. MR 0414910, 10.5802/aif.363 |
Reference:
|
[15] W. Hansen: Semi-polar sets are almost negligible.J. reine angew. Math. 314 (1980), 217-220. Zbl 0422.31009, MR 0555915 |
Reference:
|
[16] W. Hansen: Semi-polar sets and quasi-balayage.Math. Ann. 257 (1981), 495-517. Zbl 0458.31008, 10.1007/BF01465870 |
Reference:
|
[17] E. Lanconelli: Sul problema di Dirichlet per l'equazione del calore.Ann. Math. Pura ed Appl. 97(1973), 83-113. MR 0372226, 10.1007/BF02414910 |
Reference:
|
[18] I. Netuka: Thinness and the heat equation.Časopis Pěst. Mat. 99 (1974), 293-299. Zbl 0289.35037, MR 0352504 |
Reference:
|
[19] I. Netuka J. Veselý: Harmonic continuation and removable singularities in the axiomatic potential theory.Math. Ann. 234 (1978), 117-123. MR 0481063, 10.1007/BF01420962 |
Reference:
|
[20] C. J. Oxtoby: Measure and category.Springer-Verlag, Berlin, 1971. Zbl 0217.09201, MR 0584443 |
Reference:
|
[21] G. I. Petrowsky: Zur ersten Randwertaufgabe der Wärmeleitungsgleichung.Compositio Math. 7 (1935), 383 - 419. Zbl 0010.29903, MR 1556900 |
Reference:
|
[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. Zbl 0066.07804, MR 0075437, 10.1007/BF02416523 |
Reference:
|
[23] V. Sternberg: Über die Gleichung der Wärmeleitung.Math. Ann. 101 (1929), 394-398. MR 1512542, 10.1007/BF01454850 |
Reference:
|
[24] L. Stocia: On the thinness of a set at a point.Stud. Cerc. Mat. 38 (1986), 382-391. MR 0856749 |
Reference:
|
[25] K. Uchiyama: A probabilistic proof and applications of Wiener's test for the heat operator.(preprint). Zbl 0678.60066 |
Reference:
|
[26] A. N. Watson: Thermal capacity.Proc. London Math. Soc. (3) 37 (1978), 342-362. Zbl 0395.35034, MR 0507610 |
Reference:
|
[27] A. N. Watson: Thinness and boundary behaviour of potentials for the heat equation.Mathematika 32 (1985), 90-95. Zbl 0581.31005, MR 0817112, 10.1112/S0025579300010901 |
Reference:
|
[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 0425145 |
Reference:
|
[29] N. Wiener: The Dirichlet problem.J. Math. Phys. 3 (1924), 127-146. 10.1002/sapm192433127 |
. |