@article{PSMIR_1992-1993___1_A6_0, author = {Pipher, Jill}, title = {Boundary {Value} {Problems} for {Higher} {Order} {Operators} in {Lipschitz} and $C^1$ {Domains}}, journal = {Publications de l'Institut de recherche math\'ematiques de Rennes}, note = {talk:6}, pages = {1--11}, publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes}, number = {1}, year = {1992-1993}, language = {en}, url = {http://www.numdam.org/item/PSMIR_1992-1993___1_A6_0/} }
TY - JOUR AU - Pipher, Jill TI - Boundary Value Problems for Higher Order Operators in Lipschitz and $C^1$ Domains JO - Publications de l'Institut de recherche mathématiques de Rennes N1 - talk:6 PY - 1992-1993 SP - 1 EP - 11 IS - 1 PB - Département de Mathématiques et Informatique, Université de Rennes UR - http://www.numdam.org/item/PSMIR_1992-1993___1_A6_0/ LA - en ID - PSMIR_1992-1993___1_A6_0 ER -
%0 Journal Article %A Pipher, Jill %T Boundary Value Problems for Higher Order Operators in Lipschitz and $C^1$ Domains %J Publications de l'Institut de recherche mathématiques de Rennes %Z talk:6 %D 1992-1993 %P 1-11 %N 1 %I Département de Mathématiques et Informatique, Université de Rennes %U http://www.numdam.org/item/PSMIR_1992-1993___1_A6_0/ %G en %F PSMIR_1992-1993___1_A6_0
Pipher, Jill. Boundary Value Problems for Higher Order Operators in Lipschitz and $C^1$ Domains. Publications de l'Institut de recherche mathématiques de Rennes, Fascicule d'équations aux dérivées partielles, no. 1 (1992-1993), Exposé no. 6, 11 p. http://www.numdam.org/item/PSMIR_1992-1993___1_A6_0/
[A] Lectures on elliptic boundary value problems, Van Nostrand, 1965. | MR | Zbl
,[ADN1] Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I, Comm. Pure Appl. Math. 12 (1959), 623 - 727. | MR | Zbl
, and ,[ADN2] II, Comm. Pure Appl. Math. 22 (1964), 35 - 92. | MR | Zbl
, and , ibid[B] On the regularity of properties of solutions of elliptic boundary value problems, Comm. Pure Appl. Math. 9 (1956), 351 - 361. | MR | Zbl
,[C] BMO estimates for biharmonic multiple layer potentials, Studia Math. XCI (1988), 109 - 123. | MR | Zbl
,[CGI] The Dirichlet problem for the biharmonic equation in a Cl domain in the plane, Ind. U. Math. J. 32 (1983), 635 - 685. | MR | Zbl
and ,[CG2] Stress potentials on Cl domains, Jour. Math. Anal. Appl 125 (1987), no. 1, 22 - 46. | MR | Zbl
and ,[CMM] L'integrale de Cauchy definit un Operateur borne sur L2 pour les courbes lipschitziennes, Ann. of Math. 116 (1982), 361 - 387. | MR | Zbl
, and ,[Da] Elliptic boundary value problems on corner domains, Lecture Notes in Math. 1341, Springer-Verlag, 1988. | MR | Zbl
,[D] On estimates for harmonic measure, Arch. Rat. Mech, Anal. 65 (1977), 272 - 288. | MR | Zbl
,[DK] Hardy spaces and the Lp - Neumann problem for Laplace's equation in a Lipschitz domain, Annals, of Math. 125 (1987), 437 - 465. | MR | Zbl
and ,[DKV] The Dirichlet problem for the biharmonic equation in a Lipschitz domain, Ann. de l'Inst. Fourier 36 (1986), 109 - 134. | Numdam | MR | Zbl
, and ,[G] A partial differential equation arising in conformal mapping., Pac. J. Math. 1 (1951), 485 - 524. | MR | Zbl
,[Gr] Elliptic problems in nonsmooth domains, Pitman Publishing, 1985. | MR | Zbl
,[JK1] The Dirichlet problem in non-smooth domains, Ann. of Math. 113 (1981), 367 - 382. | MR | Zbl
and ,[JK2] Boundary value problems on Lipschitz domains, MAA Studies in Math. 23 (1982). | MR | Zbl
and ,[KO] Estimates near the boundary for 2nd order derivatives of solutions of the Dirichlet problem for the biharmonic equation, Att. Accad. Naz. Lincei Rend. Cl. Sei. Fis. Mat. Natur. 80 (8) (1986), 525 529. | MR | Zbl
and ,[Ko1] The strong zero theorem for an elliptic boundary value problem in a corner, Dokl. Akad. nauk. SSSR 309 (6) (1989), 1299 - 1301. | MR | Zbl
,[Ko2] The Dirichlet problem for elliptic equations in domains with conical points, Diff. Eq. 26 (1990), 739 - 747. | MR | Zbl
,[KoM1] Estimates of the Lp means and asymptotic behavior of solutions of elliptic boundary value problems in a cone, I, Seminar analysis, Akad. Wiss. DDR, Berlin (1986), 55- 91. | MR | Zbl
and ,[KoM2] II, Math. Nachr. 137 (1988), 113 - 139. | MR | Zbl
and , ibid,[KoM3] Spectral properties of operator pencils generated by elliptic boundary value problems in a cone, Funct. Anal. Appl. 22 (1988), 114 - 121. | MR | Zbl
and ,[KrM] A sharp constant in a Miranda-Agmon type inequality for solutions to elliptic equations, Soviet Math. 32 (1988), 49 -59. | MR | Zbl
and ,[MN] The apex of a cone can be irregular in Wiener's sense for a fourth-order elliptic equation, Mat. Zametki 39 (1986), 24 - 28. | MR | Zbl
and ,[MNP] On the singularities of solutions of the Dirichlet problem in the exterior of a slender cone, Math. Sb. 50 (1980), 415 - 437. | Zbl
, and ,[MP] Estimates in Lp and in Holder classes and the Mir and a-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary, Amer. Math. Soc. Transl. (2) 123 (1984), 1 - 56; Transl. from Math. Nachr. 81 (1978), 25 - 82. | MR | Zbl
and ,[MNP1] Asymptotische Theorie Elliptischer Randwertaufgaben in singular gestorten Gebieten I, Mathematische Lehrbrucher und Monographien, Akademie- Verlag, Berlin, 1991. | MR
, and ,[MR] On the Miranda-Agmon maximum principle for solutions of elliptic equations in polyhedral and polygonal domains, preprint. | MR | Zbl
and ,[O] On Green's function for the biharmonic equation in a right angle wedge, J. Math. Anal. Appl. 43 (1973), 705-716. | MR | Zbl
,[PV1] The Dirichlet problem in Lp for the biharmonic operator on Lipschitz domains, Amer. J. Math. 114 (1992), 923 -972. | MR | Zbl
and ,[PV2] Area integral estimates for the biharmonic operator in Lipschitz domains, Trans. Amer. Math. Soc. 327 (2) (1991), 903-917. | MR | Zbl
and ,[PV3] A maximum principle for biharmonic functions in non-smooth domains, Comm. Math. Helv., to appear. | MR | Zbl
and ,[PV4] Maximum principles for the polyharmonic equation on Lipschitz domains, preprint. | MR | Zbl
and ,[PV5] Dilation invariant estimates and the boundary Garding inequality for higher order elliptic operators, preprint. | MR | Zbl
and ,[S] Homogeneous boundary value problems for a polyharmonic operator with boundary conditions on thin sets, Izv. Vyssh. Vchebn. Zaved. Mat. 10 (1989), 57 - 63. | MR | Zbl
,[V1] Layer potentials and regularity for the Dirichlet problem for Laplace's equation, J.of Punct. Anal. 59 (1984), 572 - 611. | MR | Zbl
,[V2] the Dirichlet problem for the biharmonic equation in Cl domains, Ind. U. Math. J. 36 (1987), 867 - 895. | MR | Zbl
,[V3] The Dirichlet problem for the polyharmonic equation in Lipschitz domains, Ind. U. Math. J. 39 (1990), 671 702. | MR | Zbl
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