On Wiener's type regularity of a boundary point for higher order elliptic equations
- Nonlinear Analysis, Function Spaces and Applications, Publisher: Czech Academy of Sciences, Mathematical Institute(Praha), page 119-155
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topMaz'ya, Vladimir. "On Wiener's type regularity of a boundary point for higher order elliptic equations." Nonlinear Analysis, Function Spaces and Applications. Praha: Czech Academy of Sciences, Mathematical Institute, 1999. 119-155. <http://eudml.org/doc/221779>.
@inProceedings{Mazya1999,
author = {Maz'ya, Vladimir},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)},
location = {Praha},
pages = {119-155},
publisher = {Czech Academy of Sciences, Mathematical Institute},
title = {On Wiener's type regularity of a boundary point for higher order elliptic equations},
url = {http://eudml.org/doc/221779},
year = {1999},
}
TY - CLSWK
AU - Maz'ya, Vladimir
TI - On Wiener's type regularity of a boundary point for higher order elliptic equations
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 1999
CY - Praha
PB - Czech Academy of Sciences, Mathematical Institute
SP - 119
EP - 155
KW - Spring school; Proceedings; Nonlinear analysis; Function spaces; Prague (Czech Republic)
UR - http://eudml.org/doc/221779
ER -
References
top- Wiener N., The Dirichlet problem, J. Math. Phys. 3 (1924), 127–146. (1924)
- Wiener N., Certain notions in potential theory, J. Math. Phys. 3 (1924), 24–51. (1924)
- Poincaré H., Sur les équations aux derivées partielles de la physique mathématique, Amer. J. Math. 12 (1890), 211–299. MR1505534
- Zaremba S. C., Sur le principe du minimum, Bull. Acad.Sci. Cracovie, Juillet 1909. (1909)
- Lebesgue H., Sur des cas d’impossibilité du problème de Dirichlet ordinaire, C. R. des Séances de la Société Mathématique de France 17 (1913). (1913)
- 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. (1963) Zbl0116.30302MR0161019
- Fabes E. G., Jerison D., Kenig C., The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble) 32 (1982), 151–182. (1982) MR0688024
- Maso G. Dal, Mosco U., Wiener criteria and energy decay for relaxed Dirichlet problems, Arch. Rational Mech. Anal. 95 (1986), 345–387. (1986) MR0853783
- 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. (1976) MR0274948
- 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. (1977) Zbl0389.35023MR0492836
- Adams D. R., Hedberg L. I., Functions spaces and potential theory, Springer-Verlag, Berlin 1995. (1995) MR1411441
- Lindqvist P., Martio O., Two theorems of N. Wiener for solutions of quasilinear elliptic equations, Acta Math. 155 (1985), 153–171. (1985) Zbl0607.35042MR0806413
- Kilpeläinen T., Malý J., The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math. 172 (1994), 137–161. (1994)
- 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. (1997) Zbl0882.35001MR1461542
- Maz’ya V. G., Sobolev spaces, Springer-Verlag, Berlin 1985. (1985) Zbl0727.46017MR0817985
- 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). (1977)
- 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. (1979)
- 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. (1983) MR0709006
- 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. (1997) Zbl0883.35050MR1460283
- 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. (1963) MR0163053
- 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. (1967) MR0219873
- 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. (1981) MR0741698
- 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. Zbl0961.35035
- 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. (1990) MR1097961
- 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. (1981) MR0614817
- 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. (1981) MR0639068
- Maz’ya V. G. Nasarow S. A., Plamenevskii B. A., Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten, 1, Akademie-Verlag, Berlin 1991. (1991)
- 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. (1986) MR0830840
- 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. (1988) MR0947604
- Landkof N. S., Foundations of modern potential theory, Springer-Verlag, Berlin 1972. (1972) Zbl0253.31001MR0350027
- Carathéodory C., Vorlesungen über reelle Funktionen, Leipzig and Berlin, 1918. (1918)
- Vainberg M. M., Variational methods for the study of nonlinear operators, Holden-Day, San Francisco 1964. (1964) Zbl0122.35501MR0176364
- Eilertsen S., On weighted positivity of certain differential and pseudodifferential operators, Linköping Studies in Science and Technology. Theses No. 617, 1997. (1997)
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