Fegen und Dünnheit mit Anwendungen auf die Laplace-und Wärmeleitungsgleichung

Wolfhard Hansen

Annales de l'institut Fourier (1971)

  • Volume: 21, Issue: 1, page 79-121
  • ISSN: 0373-0956

Abstract

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Several properties of balayage of measures in harmonic spaces are studied. In particular, characterisations of thinness of subsets are given. For the heat equation the following result is obtained: suppose that E = R m + 1 is given the presheaf of solutions of ∑ i = 1 m ∂ u ∂ x i = ∂ u ∂ x m + 1 and B is a subset of R m × [ - ∞ , 0 ] satisfying { ( α x , α 2 t ) : ( x , t ) ∈ B , x ∈ R m , t ∈ R } ⊂ B for α > 0 arbitrarily small. Then B is thin at 0 if and only if B is polar. Similar result for the Laplace equation. At last the reduced of measures is defined and several approximation theorems on reducing and balayage of measures are proved.

How to cite

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Hansen, Wolfhard. "Fegen und Dünnheit mit Anwendungen auf die Laplace-und Wärmeleitungsgleichung." Annales de l'institut Fourier 21.1 (1971): 79-121. <http://eudml.org/doc/74030>.

@article{Hansen1971,
author = {Hansen, Wolfhard},
journal = {Annales de l'institut Fourier},
language = {ger},
number = {1},
pages = {79-121},
publisher = {Association des Annales de l'Institut Fourier},
title = {Fegen und Dünnheit mit Anwendungen auf die Laplace-und Wärmeleitungsgleichung},
url = {http://eudml.org/doc/74030},
volume = {21},
year = {1971},
}

TY - JOUR
AU - Hansen, Wolfhard
TI - Fegen und Dünnheit mit Anwendungen auf die Laplace-und Wärmeleitungsgleichung
JO - Annales de l'institut Fourier
PY - 1971
PB - Association des Annales de l'Institut Fourier
VL - 21
IS - 1
SP - 79
EP - 121
LA - ger
UR - http://eudml.org/doc/74030
ER -

References

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  1. [1] H. BAUER, Harmonische Räume und ihre Potentialtheorie. Lecture Notes in Mathematics 22, Berlin-Heidelberg New-York : Springer 1966. Zbl0142.38402
  2. [2] H. BAUER, Harmonic spaces and associated Markov processes. Centro Internazionale Matematico Estivo 1969. 
  3. [3] R.M. BLUMENTHAL and R.K. GETOOR, Markov processes and potential theory, New York : Academic Press 1968. Zbl0169.49204MR41 #9348
  4. [4] C. CONSTANTINESCU, Some properties of the balayage of measures on a harmonic space, Ann. Inst. Fourier 17/1 (1967), 273-293. Zbl0159.40804MR37 #3033
  5. [5] E.G. EFFROS and J.L. KAZDAN, On the Dirichlet problem for the heat equation, Erscheint demnächst. Zbl0216.12702
  6. [6] W. HANSEN, Potentialtheorie harmonischer Kerne, In Seminar über Potentialtheorie, Lecture Notes in Mathematics 69, Berlin-Heidelberg-New York : Springer 1968. 
  7. [7] L.L. HELMS, Introduction to potential theory, Wiley-Interscience 1969. Zbl0188.17203MR41 #5638
  8. [8] R.M. HERVE, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potential, Ann. Inst. Fourier 12, 415-571 (1962). Zbl0101.08103MR25 #3186
  9. [9] P.A. MEYER, Processus de Markov, Lecture Notes in Mathematics 26, Berlin-Heidelberg-New York : Springer 1967. Zbl0189.51403MR36 #2219

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