Boundary Value Problems for Higher Order Operators in Lipschitz and ${C}^{1}$ Domains
Publications mathématiques et informatique de Rennes no. 1  (1992-1993), Talk no. 6, 11 p.
@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 math\'ematiques et informatique de Rennes},
publisher = {D\'epartement de Math\'ematiques et Informatique, Universit\'e de Rennes},
number = {1},
year = {1992-1993},
note = {talk:6},
language = {en},
url = {http://www.numdam.org/item/PSMIR_1992-1993___1_A6_0}
}

Pipher, Jill. Boundary Value Problems for Higher Order Operators in Lipschitz and $C^1$ Domains. Publications mathématiques et informatique de Rennes, no. 1 (1992-1993), Talk no. 6, 11 p. http://www.numdam.org/item/PSMIR_1992-1993___1_A6_0/

[A] S. Agmon, Lectures on elliptic boundary value problems, Van Nostrand, 1965. | MR 178246 | Zbl 0142.37401

[ADN1] S. Agmon, A. Douglis and L. Nirenberg, 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 125307 | Zbl 0093.10401

[ADN2] S. Agmon, A. Douglis and L. Nirenberg, ibid II, Comm. Pure Appl. Math. 22 (1964), 35 - 92. | MR 162050 | Zbl 0123.28706

[B] F. Browder, On the regularity of properties of solutions of elliptic boundary value problems, Comm. Pure Appl. Math. 9 (1956), 351 - 361. | MR 90740 | Zbl 0070.09601

[C] J. Cohen, BMO estimates for biharmonic multiple layer potentials, Studia Math. XCI (1988), 109 - 123. | MR 985078 | Zbl 0682.31003

[CGI] J. Cohen and J. Gosselin, The Dirichlet problem for the biharmonic equation in a Cl domain in the plane, Ind. U. Math. J. 32 (1983), 635 - 685. | MR 711860 | Zbl 0534.31003

[CG2] J. Cohen and J. Gosselin, Stress potentials on Cl domains, Jour. Math. Anal. Appl 125 (1987), no. 1, 22 - 46. | MR 891347 | Zbl 0633.73005

[CMM] R. Coifman, A. Mcintrosh and Y. Meyer, L'integrale de Cauchy definit un Operateur borne sur L2 pour les courbes lipschitziennes, Ann. of Math. 116 (1982), 361 - 387. | MR 672839 | Zbl 0497.42012

[Da] M. Dauge, Elliptic boundary value problems on corner domains, Lecture Notes in Math. 1341, Springer-Verlag, 1988. | MR 961439 | Zbl 0668.35001

[D] B. E. J. Dahlberg, On estimates for harmonic measure, Arch. Rat. Mech, Anal. 65 (1977), 272 - 288. | MR 466593 | Zbl 0406.28009

[DK] B. E. J. Dahlberg and C. Kenig, Hardy spaces and the Lp - Neumann problem for Laplace's equation in a Lipschitz domain, Annals, of Math. 125 (1987), 437 - 465. | MR 890159 | Zbl 0658.35027

[DKV] B. Dahlberg, C. Kenig and G. Verchota, The Dirichlet problem for the biharmonic equation in a Lipschitz domain, Ann. de l'Inst. Fourier 36 (1986), 109 - 134. | Numdam | MR 865663 | Zbl 0589.35040

[G] P. Garabedian, A partial differential equation arising in conformal mapping., Pac. J. Math. 1 (1951), 485 - 524. | MR 46440 | Zbl 0045.05102

[Gr] P. Grisvard, Elliptic problems in nonsmooth domains, Pitman Publishing, 1985. | MR 775683 | Zbl 0695.35060

[JK1] D. Jerison and C. Kenig, The Dirichlet problem in non-smooth domains, Ann. of Math. 113 (1981), 367 - 382. | MR 607897 | Zbl 0434.35027

[JK2] D. Jerison and C. Kenig, Boundary value problems on Lipschitz domains, MAA Studies in Math. 23 (1982). | MR 716504 | Zbl 0529.31007

[KO] V. Kondratiev and O. Oleinik, 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 976945 | Zbl 0675.35028

[Ko1] V. Kozlov, The strong zero theorem for an elliptic boundary value problem in a corner, Dokl. Akad. nauk. SSSR 309 (6) (1989), 1299 - 1301. | MR 1045320 | Zbl 0715.35010

[Ko2] V. Kozlov, The Dirichlet problem for elliptic equations in domains with conical points, Diff. Eq. 26 (1990), 739 - 747. | MR 1073239 | Zbl 0712.35033

[KoM1] V. Kozlov and V. Maz'Ya, 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 890526 | Zbl 0631.35023

[KoM2] V. Kozlov and V. Maz'Ya, ibid, II, Math. Nachr. 137 (1988), 113 - 139. | MR 968991 | Zbl 0736.35035

[KoM3] V. Kozlov and V. Maz'Ya, Spectral properties of operator pencils generated by elliptic boundary value problems in a cone, Funct. Anal. Appl. 22 (1988), 114 - 121. | MR 947604 | Zbl 0672.35050

[KrM] G. Kresin and V. Maz'Ya, A sharp constant in a Miranda-Agmon type inequality for solutions to elliptic equations, Soviet Math. 32 (1988), 49 -59. | MR 960965 | Zbl 0672.35019

[MN] V. Maz'Ya and S. Nazarov, 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 830840 | Zbl 0604.35016

[MNP] V. Maz'Ya, S. Nazarov and B. Plamenevskii, On the singularities of solutions of the Dirichlet problem in the exterior of a slender cone, Math. Sb. 50 (1980), 415 - 437. | Zbl 0599.35056

[MP] V. G. Maz'Ya and B. A. Plamenevskii, 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 492821 | Zbl 0554.35035

[MNP1] V. Maz'Ya, S. Nazarov and B. Lamenevskii, Asymptotische Theorie Elliptischer Randwertaufgaben in singular gestorten Gebieten I, Mathematische Lehrbrucher und Monographien, Akademie- Verlag, Berlin, 1991. | MR 1101139

[MR] V. Maz'Ya and J. Rossman, On the Miranda-Agmon maximum principle for solutions of elliptic equations in polyhedral and polygonal domains, preprint. | MR 1143406 | Zbl 0753.35013

[O] S. Osher, On Green's function for the biharmonic equation in a right angle wedge, J. Math. Anal. Appl. 43 (1973), 705-716. | MR 324209 | Zbl 0263.31005

[PV1] J. Pipher and G. Verchota, The Dirichlet problem in Lp for the biharmonic operator on Lipschitz domains, Amer. J. Math. 114 (1992), 923 -972. | MR 1183527 | Zbl 0768.31006

[PV2] J. Pipher and G. Verchota, Area integral estimates for the biharmonic operator in Lipschitz domains, Trans. Amer. Math. Soc. 327 (2) (1991), 903-917. | MR 1024776 | Zbl 0774.35022

[PV3] J. Pipher and G. Verchota, A maximum principle for biharmonic functions in non-smooth domains, Comm. Math. Helv., to appear. | MR 1236761 | Zbl 0794.31005

[PV4] J. Pipher and G. Verchota, Maximum principles for the polyharmonic equation on Lipschitz domains, preprint. | MR 1361380 | Zbl 0844.35013

[PV5] J. Pipher and G. Verchota, Dilation invariant estimates and the boundary Garding inequality for higher order elliptic operators, preprint. | MR 1338674 | Zbl 0878.35035

[S] V. Slobodin, Homogeneous boundary value problems for a polyharmonic operator with boundary conditions on thin sets, Izv. Vyssh. Vchebn. Zaved. Mat. 10 (1989), 57 - 63. | MR 1044480 | Zbl 0697.31007

[V1] G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace's equation, J.of Punct. Anal. 59 (1984), 572 - 611. | MR 769382 | Zbl 0589.31005

[V2] G. Verchota, the Dirichlet problem for the biharmonic equation in Cl domains, Ind. U. Math. J. 36 (1987), 867 - 895. | MR 916748 | Zbl 0644.35039

[V3] G. Verchota, The Dirichlet problem for the polyharmonic equation in Lipschitz domains, Ind. U. Math. J. 39 (1990), 671 702. | MR 1078734 | Zbl 0724.31005