| Title:
|
On Wiener's type regularity of a boundary point for higher order elliptic equations (English) |
| Author:
|
Maz'ya, Vladimir |
| Language:
|
English |
| Journal:
|
Nonlinear Analysis, Function Spaces and Applications |
| Volume:
|
Vol. 6 |
| Issue:
|
1998 |
| Year:
|
|
| Pages:
|
119-155 |
| . |
| Category:
|
math |
| . |
| MSC:
|
31C15 |
| MSC:
|
31C45 |
| MSC:
|
35B60 |
| MSC:
|
35B65 |
| MSC:
|
35J40 |
| MSC:
|
35J67 |
| idZBL:
|
Zbl 0966.35001 |
| idMR:
|
MR1777714 |
| . |
| Date available:
|
2009-10-08T09:47:28Z |
| Last updated:
|
2012-08-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/702472 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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[4] Zaremba S. C. : Sur le principe du minimum.Bull. Acad.Sci. Cracovie, Juillet 1909. |
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[6] Littman W., Stampacchia G., Weinberger H. F. : Regular points for elliptic equations with discontinuous coefficients.Ann. Scuola Norm. Sup. Pisa Serie III, 17 (1963), 43–77. Zbl 0116.30302, MR 0161019 |
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[8] Maso G. Dal, Mosco U. : Wiener criteria and energy decay for relaxed Dirichlet problems.Arch. Rational Mech. Anal. 95 (1986), 345–387. MR 0853783 |
| Reference:
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[9] Maz’ya V. G.: On the continuity at a boundary point of solutions of quasilinear elliptic equations.Vestnik Leningrad Univ., Mat. 3 (1976), 225–242; English transl.: Vestnik Leningrad Univ. 25 (1970), 42–55. MR 0274948 |
| Reference:
|
[10] Gariepy R., Ziemer W. P. : A regularity condition at the boundary for solutions of quasilinear elliptic equations.Arch. Rational Mech. Anal. 67 (1977), 25–39. Zbl 0389.35023, MR 0492836 |
| Reference:
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[11] Adams D. R., Hedberg L. I. : Functions spaces and potential theory.Springer-Verlag, Berlin 1995. MR 1411441 |
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[12] Lindqvist P., Martio O. : Two theorems of N. Wiener for solutions of quasilinear elliptic equations.Acta Math. 155 (1985), 153–171. Zbl 0607.35042, MR 0806413 |
| Reference:
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[13] Kilpeläinen T., Malý J. : The Wiener test and potential estimates for quasilinear elliptic equations.Acta Math. 172 (1994), 137–161. |
| Reference:
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[14] Malý J., Ziemer W. P. : Regularity of solutions of elliptic partial differential equations.Mathematical Surveys and Monographs, vol. 51, American Mathematical Society, Providence, RI 1997. Zbl 0882.35001, MR 1461542 |
| Reference:
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[15] Maz’ya V. G. : Sobolev spaces.Springer-Verlag, Berlin 1985. Zbl 0727.46017, MR 0817985 |
| Reference:
|
[16] Maz’ya V. G. : On the behavior near the boundary of solutions to the Dirichlet problem for the biharmonic operator.Dokl. Akad. Nauk SSSR, 18 (1977), 15–19. English transl.: Soviet Math. Dokl. 18 (1977), 1152–1155 (1978). |
| Reference:
|
[17] Maz’ya V. G. : Behavior of solutions to the Dirichlet problem for the biharmonic operator at a boundary point.In: Equadiff IV, Lecture Notes in Math. 703, Springer-Verlag, Berlin 1979, 250–262. |
| Reference:
|
[18] Maz’ya V. G. Donchev T. : On the Wiener regularity of a boundary point for the polyharmonic operator.Dokl. Bolg. AN 36 (1983), 177–179; English transl.: Amer. Math. Soc. Transl. 137 (1987), 53–55. MR 0709006 |
| Reference:
|
[19] Maz’ya V. G. : Unsolved problems connected with the Wiener criterion.The Legacy of Norbert Wiener: A Centennial Symposium, Proc. Symp. Pure Math. vol. 60, American Mathematical Society, Providence, RI 1997, 199-208. Zbl 0883.35050, MR 1460283 |
| Reference:
|
[20] Maz’ya V. G. : On the regularity at the boundary of solutions to elliptic equations and conformal mappings.Dokl. Akad. Nauk SSSR 152 (1963), 1297–1300. English transl.: Soviet Math. Dokl. 4 (1963), 1547–1551. MR 0163053 |
| Reference:
|
[21] Maz’ya V. G. : Behavior near the boundary of solution to the Dirichlet problem for the second order elliptic operator in divergence form.Mat. Zametki 2 (1967), 209–220. MR 0219873 |
| Reference:
|
[22] Maz’ya V. G. : On the continuity modulus of a harmonic function at a boundary point.Zapiski Nauch. Sem. LOMI, Leningrad, Nauka, 135 (1981), 87–95. MR 0741698 |
| Reference:
|
[23] Björn J., Maz’ya V. G. : Capacitary estimates for solutions of the Dirichlet problem for second order elliptic equations in divergence form.Report LiTH-MAT-R-97-16, Linköping University. Zbl 0961.35035 |
| Reference:
|
[24] Maz’ya V. G. Tashchiyan G. M. : On the behavior of the gradient of a solution of the Dirichlet problem for the biharmonic equation near a boundary point of a three-dimensional domain.Sibirsk. Math. Zh. 31 (1990), 113–126. English transl.: Siberian Math. J. 31 (1991), 970–982. MR 1097961 |
| Reference:
|
[25] Maz’ya V. G. Plamenevskii B. A. : On the maximum principle for the biharmonic equation in a domain with conic points.Izv. Vyssh. Ucheb. Zaved. Mat. 2 (1981), 52–59. English transl.: Soviet Math. (Izv. VUZ) 25 (1981), 61–70. MR 0614817 |
| Reference:
|
[26] Maz’ya V. G. Plamenevskii B. A. : Properties of solutions to three-dimensional problems of elasticity theory and hydrodynamics in domains with isolated singular points.Dinamika sploshnoy sredy, Novosibirsk 50 (1981), 99–121. MR 0639068 |
| Reference:
|
[27] Maz’ya V. G. Nasarow S. A., Plamenevskii B. A. : Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten.1, Akademie-Verlag, Berlin 1991. |
| Reference:
|
[28] Maz’ya V. G. Nazarov S. A. : The vertex of a cone can be irregular in the Wiener sense for an elliptic equation of the fourth order.Mat. Zametki 39 (1986), 24–28. English transl.: Math. Notes 39 (1986), 14–16. MR 0830840 |
| Reference:
|
[29] Kozlov V. A., Maz’ya V. G. : Spectral properties of operator pencils generated by elliptic boundary value problems in a cone.Funktsional. Anal. i Prilozhen. 22 (1988), 38–46. English transl.: Functional Anal. Appl. 22 (1988), 114–121. MR 0947604 |
| Reference:
|
[30] Landkof N. S. : Foundations of modern potential theory.Springer-Verlag, Berlin 1972. Zbl 0253.31001, MR 0350027 |
| Reference:
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[31] Carathéodory C. : Vorlesungen über reelle Funktionen.Leipzig and Berlin, 1918. |
| Reference:
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[32] Vainberg M. M. : Variational methods for the study of nonlinear operators.Holden-Day, San Francisco 1964. Zbl 0122.35501, MR 0176364 |
| Reference:
|
[33] Eilertsen S. : On weighted positivity of certain differential and pseudodifferential operators.Linköping Studies in Science and Technology. Theses No. 617, 1997. |
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