On the wiener type regularity of a boundary point for the polyharmonic operator

References

• Wiener , N. 1924 . The Dirichlet problem . J. Math. and Phys , 3 : 127 – 146 . Collected works1 (1967), MIT Press, 394-413.
   Google Scholar
• Wiener , N. 1924 . Certain notions in potential theory . J. Math. Phys , 3 : 24 – 51 . Collected works 1 (1967), MIT Press, 364-391.
   Google Scholar
• Littman , W. , Stampacchia , G. and Weinberger , H.F. 1963 . Regular points for elliptic equations with discontinuous coefficients . Ann. Scuola Norm. Sup. Pisa , 17 ( III ) : 43 – 77 .
   Google Scholar
• Fabes , E.G. , Jerison , D. and Kenig , C. 1982 . The Wiener test for degenerate elliptic equations . Ann. Inst. Fourier (Grenoble) , 32 ( III ) : 151 – 182 .
   Web of Science ®Google Scholar
• Dal Maso , G. and Mosco , U. 1986 . Wiener criteria and energy decay for relaxed Dirichlet problems . Arch. Rational Mech. Anal , 95 ( III ) : 345 – 387 .
   Web of Science ®Google Scholar
• Maz'ya , V.G. 1976 . On the continuity at a boundary point of solutions of quasilinear elliptic equations . English, Vestnik Leningrad Univ. Math , 3 ( III ) : 225 – 242 . Transl. of Vestnik Leningrad Univ.25 (1970), 42-55, Russian.
   Google Scholar
• Gariepy , R. and Ziemer , W.P. 1977 . A regularity condition at the boundary for solutions of quasilinear elliptic equations . Arch. Rat. Mech. Anal , 67 ( III ) : 25 – 39 .
   Web of Science ®Google Scholar
• Lindqvist , P. and Martio , O. 1985 . Two theorems of N. Wiener for solutions of quasilinear elliptic equations . Acta Math , 155 ( III ) : 153 – 171 .
   Web of Science ®Google Scholar
• Kilpeläinen , T. and Malý , J. 1994 . The Wiener test and potential estimates for quasilinear elliptic equations . Acta Math , 172 ( III ) : 137 – 161 .
   Web of Science ®Google Scholar
• Maz'ya , V. 1997 . “ Unsolved problems connected with the Wiener criterion ” . In Proceedings of Symposia in Pure Mathematics , 199 – 208 . RI : AMS, Providence . The Legacy of Norbert Wiener: A Centennial Symposium
   Google Scholar
• Maz'ya , V.G. 1985 . Sobolev spaces , Springer-Verlag .
   Google Scholar
• Maz'ya , V.G. 1977 . On the behavior near the boundary of solutions to the Dirichlet problem for the biharmonic operator . Dokl. AN SSSR , 18 ( 4 ) : 15 – 19 .
   Google Scholar
• Maz'ya , V.G. 1979 . Behavior of solutions to the Dirichlet problem for the biharmonic operator at a boundary point . Equadiff IV, Lecture Notes Math , 703 ( 4 ) : 250 – 262 .
   Google Scholar
• Maz'ya , V.G. and Donchev , T. 1983 . On the Wiener regularity of a boundary point for the polyharmonic operator . Dokl. Bolg. AN , 36 ( 2 ) : 177 – 179 . English translation Amer. Math. Soc. Transl., 137, 2 (1987), 53-55.
   Google Scholar
• Landkof , N.S. 1972 . Foundations of modern potential theory , Springer-Verlag .
   Google Scholar
• Maz'ya , V.G. 1963 . The Dirichlet problem for elliptic equations of arbitrary order in unbounded regions . Soviet Math. Doklady , 4 : 860 – 863 .
   Google Scholar
• Maz'ya , V.G. 1963 . On the regularity at the boundary of solutions to elliptic equations and conformal mappings . Dokl. AN SSSR , 152 ( 6 ) : 1297 – 1300 .
   Google Scholar
• Caratheodory , C. 1918 . Vorlesungen über reelle Funktionen , Berlin : Leipzig .
   Google Scholar
• Vainberg , M.M. 1964 . Variational methods for the study of nonlinear operators , San Francisco : Holden-Day .
   Google Scholar
• Eilertsen , S. 1997 . On weighted positivity of certain differential and pseudodifferential operators . Linköping Studies in Science and Technology. Theses No. 617 . 1997 , Atlanta, GA.
   Google Scholar
• Maz'ya , V.G. and Nazarov , S.A. 1986 . The vertex of a cone can be irregular in the Wiener sense for an elliptic equation of the fourth order . Mat. Zametki , 7 ( 1 ) : 24 – 28 .
   Google Scholar