Sur la convergence radiale des potentiels associés à l'équation de Helmholtz

Alano Ancona; Nicolas Chevallier

Bulletin de la Société Mathématique de France (2000)

  • Volume: 128, Issue: 2, page 249-281
  • ISSN: 0037-9484

How to cite

top

Ancona, Alano, and Chevallier, Nicolas. "Sur la convergence radiale des potentiels associés à l'équation de Helmholtz." Bulletin de la Société Mathématique de France 128.2 (2000): 249-281. <http://eudml.org/doc/87828>.

@article{Ancona2000,
author = {Ancona, Alano, Chevallier, Nicolas},
journal = {Bulletin de la Société Mathématique de France},
keywords = {radial limits; potentials; Helmholtz equation; fine limits},
language = {fre},
number = {2},
pages = {249-281},
publisher = {Société mathématique de France},
title = {Sur la convergence radiale des potentiels associés à l'équation de Helmholtz},
url = {http://eudml.org/doc/87828},
volume = {128},
year = {2000},
}

TY - JOUR
AU - Ancona, Alano
AU - Chevallier, Nicolas
TI - Sur la convergence radiale des potentiels associés à l'équation de Helmholtz
JO - Bulletin de la Société Mathématique de France
PY - 2000
PB - Société mathématique de France
VL - 128
IS - 2
SP - 249
EP - 281
LA - fre
KW - radial limits; potentials; Helmholtz equation; fine limits
UR - http://eudml.org/doc/87828
ER -

References

top
  1. [An1] ANCONA (A.). — Théorie du potentiel sur les graphes et les variétés, in École d'été de Probabilités de Saint-Flour XVIII — 1988, Lecture Notes in Math. 1427, Springer-Verlag, 1990, p. 5-112. Zbl0719.60074
  2. [An2] ANCONA (A.). — Negatively curved manifolds, elliptic operators and the Martin boundary, Ann. of Math., t. 125, 1987, p. 495-536. Zbl0652.31008MR88k:58160
  3. [An3] ANCONA (A.). — First eigenvalues and comparisons of Green's functions for elliptic operators on manifolds or domains, J. Anal. Math., t. 72, 1997, p. 45-92. Zbl0944.58016MR98i:58212
  4. [Ber] BERG (C.). — Potential theory on the infinite dimensional torus, Invent. Math., t. 32 (1), 1976, p. 49-100. Zbl0371.31007MR53 #5915
  5. [Bre] BRELOT (M.). — Axiomatique des fonctions harmoniques. — Les Presses de l'Université de Montréal, 1969. Zbl0148.10401MR40 #393
  6. [Che] CHEVALLIER (N.). — A note on lower limit of series and potential theory, Proc. Royal Soc. Edinburgh, t. 121A, 1992, p. 273-277. Zbl0763.40001MR93j:31010
  7. [Da1] DAHLBERG (B.E.J.). — On estimates of harmonic measure, Arch. Rat. Mech. Anal., t. 1965, 1977, p. 272-288. Zbl0406.28009MR57 #6470
  8. [Da2] DAHLBERG (B.E.J.). — On the existence of radial boundary values for functions subharmonic in a Lipschitz domain, Indiana Univ. Math. J., t. 27, n° 3, 1978, p. 515-526. Zbl0402.31011MR58 #6292
  9. [Den] DENY (J.). — Un théorème sur les ensembles effilés, Ann. Univ. Grenoble Sect. Sci. Math. Phys., t. 23, 1948, p. 139-142. Zbl0030.05602MR9,509a
  10. [Doo] DOOB (J.L.). — Some classical function theory theorems and their modern versions, Ann. Inst. Fourier, t. 15 (1), 1965, p. 115-136. Zbl0154.07503MR34 #2923
  11. [Hei] HEINTZE (E.). — On homogeneous manifolds of negative curvature, Math. Ann., t. 211, 1974, p. 23-34. Zbl0273.53042MR50 #5695
  12. [Her] HERVÉ (R.-M.). — Recherche sur la théorie axiomatique des fonctions surharmoniques et du Potentiel, Ann. Inst. Fourier, t. XII, 1962, p. 415-471. Zbl0101.08103MR25 #3186
  13. [J-K] JERISON (D.), KENIG (C.). — Positive harmonic functions in non tangentially accessible domains, Advances in Math., t. 46, 1982, p. 80-147. Zbl0514.31003MR84d:31005b
  14. [Kan] KANNAI (Y.). — Off diagonal short time asymptotics for fundamental solutions of diffusions equations, Commun. Partial Differ. Equations, t. 2 (8), 1977, p. 781-830. Zbl0381.35039MR58 #29247
  15. [KW] KAUFMAN (R.), WU (J.-M.). — Parabolic Potential theory, J. Diff. Equations, t. 43, 1982, p. 204-234. Zbl0534.31005MR83d:31006
  16. [KT] KORANYI (A.), TAYLOR (J.C.). — Fine convergence and parabolic convergence for the Helmholtz equation and the heat equation, Illinois J. Math., t. 27 (1), 1983, p. 77-93. Zbl0488.31004MR85a:31008
  17. [Lel] LELONG-FERRAND (J.). — Étude au voisinage d'un point frontière des fonctions surharmoniques positives dans un demi-espace, Ann. Sci. École Norm. Sup., t. 66, 1947, p. 125-159. Zbl0033.37301MR11,176f
  18. [Lin] LINDEN (O.). — Fatou theorem for eigenfunctions of the Laplace-Beltrami operator. — Thesis, Yeshiva University, 1977. 
  19. [Lit] LITTLEWOOD (J.E.). — On functions subharmonic in a circle, II, Proc. Lond. Math. Soc., t. 28 (2), 1928, p. 383-394. Zbl54.0516.04JFM54.0516.04
  20. [LMT] LYONS (T.J.), MACGIBBON (K.B.), TAYLOR (J.C.). — Projection theorems for hitting probabilities and a theorem of Littlewood, J. Funct. Anal., t. 59, 1984, p. 470-489. Zbl0566.58036MR86c:31002
  21. [Naï] NAÏM (L.). — Sur le rôle de la frontière de R.S. Martin dans la théorie du potentiel, Ann. Inst. Fourier, t. 7, 1957, p. 183-281. Zbl0086.30603MR20 #6608
  22. [TW] TAYLOR (S.J.), WATSON (N.A.). — A Hausdorff measure classification of polar sets for the heat equation, Math. Proc. Cambridge Phil. Soc., t. 97, 1985, p. 325-344. Zbl0584.31006MR86m:35077
  23. [Zha] ZHAO (S.). — Boundary behavior of subharmonic functions in nontangential accessible domains, Studia Math., t. 108 (1), 1994, p. 25-48. Zbl0863.31008MR94k:31009

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.