Exceptional boundary points for the nondivergence equation which are regular for the Laplace equation — and vice-versa

Keith Miller

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1968)

  • Volume: 22, Issue: 2, page 315-330
  • ISSN: 0391-173X

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Miller, Keith. "Exceptional boundary points for the nondivergence equation which are regular for the Laplace equation — and vice-versa." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 22.2 (1968): 315-330. <http://eudml.org/doc/83460>.

@article{Miller1968,
author = {Miller, Keith},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {partial differential equations},
language = {eng},
number = {2},
pages = {315-330},
publisher = {Scuola normale superiore},
title = {Exceptional boundary points for the nondivergence equation which are regular for the Laplace equation — and vice-versa},
url = {http://eudml.org/doc/83460},
volume = {22},
year = {1968},
}

TY - JOUR
AU - Miller, Keith
TI - Exceptional boundary points for the nondivergence equation which are regular for the Laplace equation — and vice-versa
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1968
PB - Scuola normale superiore
VL - 22
IS - 2
SP - 315
EP - 330
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/83460
ER -

References

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  1. [1] Aleksandrov, A.D.Uniqueness conditions and bounds for the solution of the Dirichlet problem (in Russian), Vestnich Leningrad. Univ. Ser. Mat. Mech. Astron., 18 (1963) no. 3, pp. 5-29. MR164135
  2. [2] Birkhoff, G., and Rota, G., Ordinary differential equations, Ginn and Co., Boston (1962), p. 259. Zbl0102.29901MR138810
  3. [3] Coddington, E., and Levinson, N., Theory of ordinary differential equations, McGraw-Hill, New York (1955), see pp. 132-135. Zbl0064.33002MR69338
  4. [4] Courant, R., and Hilbert, D., Methods of mathematical physics, Vol. 2, Interscience, New York (1961), see p. 303 and p. 339. Zbl0099.29504
  5. [5] Gilbarg, D., and Serrin, J., On isolated singularities of solutions of second order elliptic differential equations, J. d'Analyse Math., Vol. 4 (1956), pp. 309-340. Zbl0071.09701MR81416
  6. [6] Hervé, R.M., Recherches axiomatique sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, Grenoble12 (1962), pp. 415-571. Zbl0101.08103MR139756
  7. [7] Kellog, O.D., Foundations of potential theory, Dover, New York (1953), see p. 334 and p. 330. Zbl0053.07301
  8. [8] Lebesgue, H., Conditions de regularitè, conditions d'irrégularité, conditions d'impossibilitè dans le problème de Dirichlet, Comptes Rendus, Vol. 178 (1924), pp. 352-354. Zbl50.0332.01JFM50.0332.01
  9. [9] Littman, W., Stampacchia, G., and Weinberger, H.F., Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. di Pisa, XVII (1963) pp. 45-79. Zbl0116.30302MR161019
  10. [10] Miller, K., Barriers on cones for uniformly elliptic operators, Ann. Mat. Pura Appl., LXXVI (1967), pp. 93-105. Zbl0149.32101MR221087
  11. [11] Miller. K., Existence theory for certain ordinary diffenential equations with a monotone singularity, to appear in Proc. Amer. Math. Soc. Zbl0159.11503MR226082
  12. [12] Miller, K., Extremal barriers on cones with Phragmen-Lindelöf theorems and other applications, (to appear). Zbl0231.35004MR316884
  13. [13] Pucci, C., Operatori ellittici estremanti, Ann. Mat. Pura Appl., Vol. 72 (1966), pp. 141-170. Zbl0154.12402MR208150
  14. [14] Pucci, C., Limitazioni per soluzioni di equazioni ellittiche, Ann. Mat. Pura Appl., Vol. 74 (1966), pp. 15-30. Zbl0144.35801MR214905

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