Keywords: third problem; Laplace equation; continuous extendibility
@article{CMJ_2003_53_3_a14,
author = {Medkov\'a, Dagmar},
title = {Continuous extendibility of solutions of the third problem for the {Laplace} equation},
journal = {Czechoslovak Mathematical Journal},
pages = {669--688},
year = {2003},
volume = {53},
number = {3},
mrnumber = {2000062},
zbl = {1080.35009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2003_53_3_a14/}
}
Medková, Dagmar. Continuous extendibility of solutions of the third problem for the Laplace equation. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 669-688. http://geodesic.mathdoc.fr/item/CMJ_2003_53_3_a14/
[1] V. Anandam and M. A. Al-Gwaiz: Global representation of harmonic and biharmonic functions. Potential Anal. 6 (1997), 207–214. | DOI | MR
[2] V. Anandam and M. Damlakhi: Harmonic singularity at infinity in $R^n$. Real Anal. Exchange 23 (1997/8), 471–476. | MR
[3] 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
[4] Yu. D. Burago and V. G. Maz’ya: Potential theory and function theory for irregular regions. Zapiski Naučnyh Seminarov LOMI 3 (1967), 1–152 (In Russian).
[5] L. E. Fraenkel: Introduction to Maximum Principles and Symmetry in Elliptic Problems. Cambridge Tracts in Mathematics 128. Cambridge University Press, 2000. | MR
[6] 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
[7] 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, .
[8] 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, .
[9] 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, .
[10] L. L. Helms: Introduction to Potential Theory. Pure and Applied Mathematics 22. John Wiley & Sons, 1969. | MR
[11] J. Král: Integral Operators in Potential Theory. Lecture Notes in Mathematics 823. Springer-Verlag, Berlin, 1980. | MR
[12] J. Král: The Fredholm method in potential theory. Trans. Amer. Math. Soc. 125 (1966), 511–547. | DOI | MR
[13] J. Král and W. L. Wendland: Some examples concerning applicability of the Fredholm-Radon method in potential theory. Aplikace matematiky 31 (1986), 293–308. | MR
[14] N. L. Landkof: Fundamentals of Modern Potential Theory. Izdat. Nauka, Moscow, 1966. (Russian) | MR
[15] 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
[16] D. Medková: Solution of the Robin problem for the Laplace equation. Appl. Math. 43 (1998), 133–155. | DOI | MR
[17] D. Medková: Solution of the Neumann problem for the Laplace equation. Czechoslovak Math. J. 48(123) (1998), 768–784. | DOI | MR
[18] D. Medková: Continuous extendibility of solutions of the Neumann problem for the Laplace equation. Czechoslovak Math. J 53(128) (2003), 377–395. | DOI | MR
[19] J. Nečas: Les méthodes directes en théorie des équations élliptiques. Academia, Prague, 1967. | MR
[20] I. Netuka: Fredholm radius of a potential theoretic operator for convex sets. Čas. pěst. mat. 100 (1975), 374–383. | MR | Zbl
[21] I. Netuka: Generalized Robin problem in potential theory. Czechoslovak Math. J. 22(97) (1972), 312–324. | MR | Zbl
[22] I. Netuka: An operator connected with the third boundary value problem in potential theory. Czechoslovak Math. J. 22(97) (1972), 462–489. | MR | Zbl
[23] I. Netuka: The third boundary value problem in potential theory. Czechoslovak Math. J. 22(97) (1972), 554–580. | MR | Zbl
[24] I. Netuka: Continuity and maximum principle for potentials of signed measures. Czechoslovak Math. J. 25(100) (1975), 309–316. | MR | Zbl
[25] 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
[26] 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
[27] G. E. Shilov: Mathematical analysis. Second special course. Nauka, Moskva, 1965. (Russian) | MR
[28] 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
[29] M. Schechter: Principles of Functional Analysis. Academic press, New York-London, 1973. | MR
[30] W. P. Ziemer: Weakly Differentiable Functions. Springer Verlag, 1989. | MR | Zbl