Keywords: Neumann problem; Laplace equation; continuous extendibility
@article{CMJ_2003_53_2_a12,
author = {Medkov\'a, Dagmar},
title = {Continuous extendibility of solutions of the {Neumann} problem for the {Laplace} equation},
journal = {Czechoslovak Mathematical Journal},
pages = {377--395},
year = {2003},
volume = {53},
number = {2},
mrnumber = {1983459},
zbl = {1075.35508},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2003_53_2_a12/}
}
Medková, Dagmar. Continuous extendibility of solutions of the Neumann problem for the Laplace equation. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 2, pp. 377-395. http://geodesic.mathdoc.fr/item/CMJ_2003_53_2_a12/
[1] T. S. Angell, R. E. Kleinman and J. Král: Layer potentials on boundaries with corners and edges. Čas. pěst. mat. 113 (1988), 387–402. | MR
[2] H. Bauer: Harmonische Räume und ihre Potentialtheorie. Springer Verlag, Berlin, 1966. | MR | Zbl
[3] N. Boboc, C. Constantinescu and A. Cornea: On the Dirichlet problem in the axiomatic theory of harmonic functions. Nagoya Math. J. 23 (1963), 73–96. | MR
[4] M. Brelot: Éléments de la théorie classique du potentiel. Centre de documentation universitaire, Paris, 1961. | MR
[5] Yu. D. Burago and V. G. Maz’ya: Potential theory and function theory for irregular regions. Zapiski Naučnyh Seminarov LOMI 3 (1967), 1–152. (Russian)
[6] E. De Giorgi: Nuovi teoremi relativi alle misure $(r-1)$-dimensionali in uno spazi ad $r$ dimensioni. Ricerche Mat. 4 (1955), 95–113. | MR
[7] E. B. Fabes, M. Jodeit and N. M. Riviére: Potential techniques for boundary value problems in $C^1$ domains. Acta Math. 141 (1978), 165–186. | DOI | MR
[8] N. V. Grachev and V. G. Maz’ya: On the Fredholm radius for operators of the double layer potential type on piecewise smooth boundaries. Vest. Leningrad. Univ. 19 (1986), 60–64. | MR
[9] N. V. Grachev and V. G. Maz’ya: Invertibility of Boundary Integral Operators of Elasticity on Surfaces with Conic Points. Report LiTH-MAT-R-91-50, Linköping Univ., Sweden.
[10] N. V. Grachev and V. G. Maz’ya: Solvability of a Boundary Integral Equation on a Polyhedron. Report LiTH-MAT-R-91-50, Linköping Univ., Sweden.
[11] N. V. Grachev and V. G. Maz’ya: Estimates for Kernels of the Inverse Operators of the Integral Equations of Elasticity on Surfaces with Conic Points. Report LiTH-MAT-R-91-06. Linköping Univ., Sweden.
[12] H. Heuser: Funktionalanalysis. Teubner, Stuttgart, 1975. | MR | Zbl
[13] V. Kordula, V. Müller and V. Rakočević: On the semi-Browder spectrum. Studia Math. 123 (1997), 1–13. | MR
[14] J. Köhn and M. Sieveking: Zum Cauchyschen und Dirichletschen Problem. Math. Ann. 177 (1968), 133–142. | DOI | MR
[15] J. Král: Integral Operators in Potential Theory. Lecture Notes in Mathematics 823. Springer-Verlag, Berlin, 1980. | MR
[16] J. Král: The Fredholm method in potential theory. Trans. Amer. Math. Soc. 125 (1966), 511–547. | DOI | MR
[17] J. Král: Problème de Neumann faible avec condition frontière dans $L^1$. Séminaire de Théorie du Potentiel (Université Paris VI) No. 9, Lecture Notes in Mathematics Vol. 1393, Springer-Verlag, 1989, pp. 145–160.
[18] J. Král and W. L. Wendland: Some examples concerning applicability of the Fredholm-Radon method in potential theory. Appl. Math. 31 (1986), 293–308. | MR
[19] N. L. Landkof: Fundamentals of Modern Potential Theory. Izdat. Nauka, Moscow, 1966. (Russian) | MR
[20] D. Medková: The third boundary value problem in potential theory for domains with a piecewise smooth boundary. Czechoslovak Math. J. 47(122) (1997), 651–679. | DOI | MR
[21] D. Medková: Solution of the Robin problem for the Laplace equation. Appl. Math. 43 (1998), 133–155. | DOI | MR
[22] D. Medková: Solution of the Neumann problem for the Laplace equation. Czechoslovak Math. J. 48(123) (1998), 768–784. | DOI | MR
[23] I. Netuka: Fredholm radius of a potential theoretic operator for convex sets. Čas. pěst. mat. 100 (1975), 374–383. | MR | Zbl
[24] I. Netuka: Generalized Robin problem in potential theory. Czechoslovak Math. J. 22(97) (1972), 312-324. | MR | Zbl
[25] I. Netuka: An operator connected with the third boundary value problem in potential theory. Czechoslovak Math. J. 22(97) (1972), 462–489. | MR | Zbl
[26] I. Netuka: The third boundary value problem in potential theory. Czechoslovak Math. J. 22(97) (1972), 554–580. | MR | Zbl
[27] I. Netuka: Continuity and maximum principle for potentials of signed measures. Czechoslovak Math. J. 25(100) (1975), 309–316. | MR | Zbl
[28] A. Rathsfeld: The invertibility of the double layer potential in the space of continuous functions defined on a polyhedron. The panel method. Appl. Anal. 45 (1992), 1–4, 135–177. | DOI | MR
[29] A. Rathsfeld: The invertibility of the double layer potential operator in the space of continuous functions defined over a polyhedron. The panel method. Erratum. Appl. Anal. 56 (1995), 109–115. | DOI | MR | Zbl
[30] Ch. G. Simader: The weak Dirichlet and Neumann problem for the Laplacian in $L^q$ for bounded and exterior domains. Applications. Nonlinear analysis, function spaces and applications, Vol. 4, Proc. Spring School, Roudnice nad Labem (Czech, 1990), Teubner-Texte Math. 119, 1990, pp. 180–223. | MR
[31] Ch. G. Simader and H. Sohr: The Dirichlet problem for the Laplacian in bounded and unbounded domains. Pitman Research Notes in Mathematics Series 360, Addison Wesley Longman Inc., 1996. | MR
[32] M. Schechter: Principles of Functional Analysis. Academic Press, 1973. | MR
[33] W. P. Ziemer: Weakly Differentiable Functions. Springer Verlag, 1989. | MR | Zbl