The Wiener criterion and quasilinear uniformly elliptic equations

J. H. Michael; William P. Ziemer

Annales de l'I.H.P. Analyse non linéaire (1987)

  • Volume: 4, Issue: 5, page 453-486
  • ISSN: 0294-1449

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Michael, J. H., and Ziemer, William P.. "The Wiener criterion and quasilinear uniformly elliptic equations." Annales de l'I.H.P. Analyse non linéaire 4.5 (1987): 453-486. <http://eudml.org/doc/78140>.

@article{Michael1987,
author = {Michael, J. H., Ziemer, William P.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {quasilinear; divergence form; Dirichlet problem; Wiener solution},
language = {eng},
number = {5},
pages = {453-486},
publisher = {Gauthier-Villars},
title = {The Wiener criterion and quasilinear uniformly elliptic equations},
url = {http://eudml.org/doc/78140},
volume = {4},
year = {1987},
}

TY - JOUR
AU - Michael, J. H.
AU - Ziemer, William P.
TI - The Wiener criterion and quasilinear uniformly elliptic equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1987
PB - Gauthier-Villars
VL - 4
IS - 5
SP - 453
EP - 486
LA - eng
KW - quasilinear; divergence form; Dirichlet problem; Wiener solution
UR - http://eudml.org/doc/78140
ER -

References

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  1. [GZ] R. Gariepy and P. Ziemer, A Regularity Condition at the Boundary for solutions of Quasilinear Elliptic Equations, Arch. Rat. Mech. Anal., Vol. 67, 1977, pp. 372. Zbl0389.35023MR492836
  2. [GT] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren der mathématischen Wissenschaften, Vol. 224, Springer-Verlag. Zbl0361.35003MR473443
  3. [HW] L.I. Hedberg and Th.H. Wolff, Thin Sets in Nonlinear Potential Theory, Ann. Inst. Fourier (Grenoble), Vol. 33, 1983, No 4, pp. 161-187. Zbl0508.31008MR727526
  4. [LU] O.A. Ladyzenskaya and N.N. Ural'tseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
  5. [MA] V.G. Maz'ja, On the Continuity at a Boundary Point of Solutions of Quasilinear Elliptic Equations, Vestnik Leningrad Univ., Vol. 25, No. 13, 1970; Vestnik Leningrad Univ. Math., Vol. 3, 1976. Zbl0252.35024MR274948
  6. [MI1] J.H. Michael, A General Theory for Linear Elliptic Partial Differential Equations, Journal of differential equations, Vol. 23, 1977, pp. 1-29. Zbl0299.35037MR425346
  7. [MI2] J.H. Michael, The Dirichlet Problem for Quasilinear Uniformly Elliptic Equations, Nonlinear Analysis, Vol. 9, 1985, pp. 455-467. Zbl0526.35031MR785717
  8. [MZ1] J.H. Michael and W.P. Ziemer, A Lusin Type Approximation of Sobolev Functions by Smooth Functions, Contemporary Mathematics, Vol. 42, 1985, pp. 135-167. Zbl0592.41031MR807986
  9. [MZ2] J.H. Michael and W.P. Ziemer, Interior Regularity for Solutions to Obstacle Problems, J. Non-linear Anal. (to appear). Zbl0603.49006MR869551
  10. [W1] N. Wiener, The Dirichlet Problem, J. Math. and Phys., Vol. 3, 1924, pp. 127-146. Zbl51.0361.01JFM51.0361.01
  11. [W2] N. Wiener, Certain Notion in Potential Theory, J. Math. and Phys., Vol. 3, 1924, pp. 24-51. JFM50.0646.03
  12. [Z] W.P. Ziemer, The Dirichlet Problem for Euler-Lagrange Equations on Arbitrary Domains, J. London Math. Soc., (2), Vol. 19, 1979, pp. 481-487. Zbl0458.35037MR540064

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