Nonequivalence of regular boundary points for the Laplace and nondivergence equations, even with continuous coefficients

Keith Miller

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1970)

  • Volume: 24, Issue: 1, page 159-163
  • ISSN: 0391-173X

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Miller, Keith. "Nonequivalence of regular boundary points for the Laplace and nondivergence equations, even with continuous coefficients." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 24.1 (1970): 159-163. <http://eudml.org/doc/83518>.

@article{Miller1970,
author = {Miller, Keith},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {1},
pages = {159-163},
publisher = {Scuola normale superiore},
title = {Nonequivalence of regular boundary points for the Laplace and nondivergence equations, even with continuous coefficients},
url = {http://eudml.org/doc/83518},
volume = {24},
year = {1970},
}

TY - JOUR
AU - Miller, Keith
TI - Nonequivalence of regular boundary points for the Laplace and nondivergence equations, even with continuous coefficients
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1970
PB - Scuola normale superiore
VL - 24
IS - 1
SP - 159
EP - 163
LA - eng
UR - http://eudml.org/doc/83518
ER -

References

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  1. [1] Gilbarg, D. and Serrin, J., On isolated singularities of solutions of second order elliptic differential equations, J. Analyse Math., vol. 4 (1956), pp. 309-340. Zbl0071.09701MR81416
  2. [2] Hervé, R.M., Recherches axiomatique sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier, Grenoble12 (1962), pp. 415-571. Zbl0101.08103MR139756
  3. [3] Krylov, N.V., On solutions of elliptic equations of the second order (Russian), Uspehi Mat Nauk., Vol. 21 (1966), no. 2 (128) pp. 233-235. MR193764
  4. [4] Landis, E.M., s-capacity and the behavior of a solution of a second-order elliptic equation with discontinuous coefficients in the neighborhood of a boundary point, Dokl. Akad. Nauk. SSSR, 180 (1968); translated in Soviet Math. Dokl, 9 (1968), pp. 582-586. Zbl0167.40101MR229960
  5. [5] Littman, W., Stampacchia, G., and Weinberger, H.F., Regular points for elliptic equations with discontinuous coefflcients, Ann. Scuola Norm. Sup. diPisa, XVII (1963) pp. 45-79. Zbl0116.30302MR161019
  6. [6] Miller, K, Barriers on cones for uniformly elliptic operators, Ann. Mat. Pura Appl., LXXVI (1967), pp. 93-105. Zbl0149.32101MR221087
  7. [7] Miller, K., Exceptional boundary points for the nondivergence equation which are regular for the Laplace equation-and vice-versa, Ann. Scuola Norm. Sup. diPisa, XXIV (1968), pp. 315-330. Zbl0164.13102MR229961
  8. [8] Oleinik, O.A., On the Dirichlet problem for equations of elliptic type, (Russian), Math. Sb. vol. 24 (66) (1949), pp. 3-14, Math. Review 10 # 713. Zbl0035.18701MR30101
  9. [9] Zograf, O.N., An example of an elliptic second-order equation with continuous coefficients for which the regularity conditions of a boundary point for the Dirichlet problem are different from similar conditions for Laplace's equation, (Russian), Vestnik Moscow Univ. Serie 1: Matematika, mekhanika, no. 2 (1969), pp. 30-39. Zbl0172.14702MR255981

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