Voir la notice de l'article provenant de la source Czech Digital Mathematics Library
MR ZblMedková, Dagmar. Boundedness of the solution of the third problem for the Laplace equation. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 317-340. http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a3/
@article{CMJ_2005_55_2_a3,
author = {Medkov\'a, Dagmar},
title = {Boundedness of the solution of the third problem for the {Laplace} equation},
journal = {Czechoslovak Mathematical Journal},
pages = {317--340},
year = {2005},
volume = {55},
number = {2},
mrnumber = {2137140},
zbl = {1081.35013},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_2_a3/}
}
[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] M. Brelot: Éléments de la théorie classique du potentiel. Centre de documentation universitaire, Paris, 1961. | MR
[3] 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)
[4] H. Federer and W. P. Ziemer: The Lebesgue set of a function whose partial derivatives are $p$-th power summable. Indiana Univ. Math. J. 22 (1972), 139–158. | MR
[5] W. H. Fleming: Functions whose partial derivatives are measures. Illinois J. Math. 4 (1960), 452–478. | DOI | MR | Zbl
[6] L. E. Fraenkel: Introduction to Maximum Principles and Symmetry in Elliptic Problems. Cambridge Tracts in Mathematics 128. Cambridge University Press, Cambridge, 2000. | MR
[7] 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
[8] 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., Linköping.
[9] 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., Linköping.
[10] 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., Linköping.
[11] L. L. Helms: Introduction to Potential Theory. Pure and Applied Mathematics 22. John Wiley & Sons, , 1969. | MR
[12] J. Král: Integral Operators in Potential Theory. Lecture Notes in Mathematics 823. Springer-Verlag, Berlin, 1980. | MR
[13] J. Král: The Fredholm method in potential theory. Trans. Amer. Math. Soc. 125 (1966), 511–547. | DOI | MR
[14] 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
[15] N. L. Landkof: Fundamentals of Modern Potential Theory. Izdat. Nauka, Moscow, 1966. (Russian) | MR
[16] D. Medková: The third boundary value problem in potential theory for domains with a piecewise smooth boundary. Czechoslovak Math. J. 47 (1997), 651–679. | DOI | MR
[17] D. Medková: Solution of the Robin problem for the Laplace equation. Appl. Math. 43 (1998), 133–155. | DOI | MR
[18] D. Medková: Solution of the Neumann problem for the Laplace equation. Czechoslovak Math. J. 48 (1998), 768–784. | DOI
[19] D. Medková: Continuous extendibility of solutions of the Neumann problem for the Laplace equation. Czechoslovak Math. J 53 (2003), 377–395. | DOI | MR
[20] D. Medková: Continuous extendibility of solutions of the third problem for the Laplace equation. Czechoslovak Math. J 53 (2003), 669–688. | DOI | MR
[21] D. Medková: Solution of the Dirichlet problem for the Laplace equation. Appl. Math. 44 (1999), 143–168. | DOI
[22] J. Nečas: Les méthodes directes en théorie des équations élliptiques. Academia, Prague, 1967. | 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. 2(97) (1972), 554–580. | MR | Zbl
[27] A. Rathsfeld: The invertibility of the double layer potential in the space of continuous functions defined on a polyhedron. The panel method. Applicable Analysis 45 (1992), 135–177. | DOI | MR
[28] A. Rathsfeld: The invertibility of the double layer potential operator in the space of continuous functions defined over a polyhedron. The panel method. Erratum. Applicable Analysis 56 (1995), 109–115. | DOI | MR | Zbl
[29] M. Schechter: Principles of Functional Analysis. Academic Press, , 1973. | MR
[30] W. P. Ziemer: Weakly Differentiable Functions. Springer-Verlag, , 1989. | MR | Zbl