On Wiener's type regularity of a boundary point for higher order elliptic equations

Maz'ya, Vladimir

Nonlinear Analysis, Function Spaces and Applications, GDML_Books, (1999), p. 119-155 / Harvested from

Détail

MR MR1777714 | Zbl 0966.35001

EUDML-ID : urn:eudml:doc:221779
Mots clés:

Bibliographie

Poincaré H. Sur les équations aux derivées partielles de la physique mathématique, Amer. J. Math. 12 (1890), 211–299. | MR 1505534

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

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)

Carathéodory C. Vorlesungen über reelle Funktionen, Leipzig and Berlin, 1918. (1918)

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)

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) | MR 0161019 | Zbl 0116.30302

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) | MR 0163053

Vainberg M. M. Variational methods for the study of nonlinear operators, Holden-Day, San Francisco 1964. (1964) | MR 0176364 | Zbl 0122.35501

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) | MR 0219873

Landkof N. S. Foundations of modern potential theory, Springer-Verlag, Berlin 1972. (1972) | MR 0350027 | Zbl 0253.31001

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) | MR 0274948

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) | MR 0492836 | Zbl 0389.35023

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. On the continuity modulus of a harmonic function at a boundary point, Zapiski Nauch. Sem. LOMI, Leningrad, Nauka, 135 (1981), 87–95. (1981) | MR 0741698

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) | MR 0614817

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) | MR 0639068

Fabes E. G.; Jerison D.; Kenig C. The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble) 32 (1982), 151–182. (1982) | MR 0688024

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) | MR 0709006

Lindqvist P.; Martio O. Two theorems of N. Wiener for solutions of quasilinear elliptic equations, Acta Math. 155 (1985), 153–171. (1985) | MR 0806413 | Zbl 0607.35042

Maz’ya V. G. Sobolev spaces, Springer-Verlag, Berlin 1985. (1985) | MR 0817985 | Zbl 0727.46017

Maso G. Dal; Mosco U. Wiener criteria and energy decay for relaxed Dirichlet problems, Arch. Rational Mech. Anal. 95 (1986), 345–387. (1986) | MR 0853783

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) | MR 0830840

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) | MR 0947604

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) | MR 1097961

Maz’ya V. G. Nasarow S. A.; Plamenevskii B. A. Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten, 1, Akademie-Verlag, Berlin 1991. (1991)

Kilpeläinen T.; Malý J. The Wiener test and potential estimates for quasilinear elliptic equations, Acta Math. 172 (1994), 137–161. (1994)

Adams D. R.; Hedberg L. I. Functions spaces and potential theory, Springer-Verlag, Berlin 1995. (1995) | MR 1411441

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) | MR 1461542 | Zbl 0882.35001

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) | MR 1460283 | Zbl 0883.35050

Eilertsen S. On weighted positivity of certain differential and pseudodifferential operators, Linköping Studies in Science and Technology. Theses No. 617, 1997. (1997)