Dauge, M.; Nicaise, S.; Bourlard, M.; Lubuma, J. Mbaro-Saman Coefficients des singularités pour des problèmes aux limites elliptiques sur un domaine à points coniques. II: Quelques opérateurs particuliers. (Singularity coefficients for boundary values in domains with conical points. II: Some particular operators). (French) Zbl 0723.35035 RAIRO, Modélisation Math. Anal. Numér. 24, No. 3, 343-367 (1990). Summary: [For part I see ibid. 24, No.1, 27-52 (1990; Zbl 0691.35023).] In the first part of this work, we have given general formulae for the coefficients of the singularities for the Dirichlet problem associated to any elliptic operator. Now, we make those formulae more precise for the Laplace operator on a cone, the biharmonic operator and the Helmholtz operator on a polygon; then, we extend our results to another boundary value problem: the mixed oblique derivative problem on a polygon. Cited in 1 ReviewCited in 11 Documents MSC: 35J67 Boundary values of solutions to elliptic equations and elliptic systems 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs Keywords:singularities; Dirichlet problem; Laplace operator; biharmonic operator; Helmholtz operator; oblique derivative problem Citations:Zbl 0691.35023 PDFBibTeX XMLCite \textit{M. Dauge} et al., RAIRO, Modélisation Math. Anal. Numér. 24, No. 3, 343--367 (1990; Zbl 0723.35035) Full Text: DOI EuDML References: [1] M. DAUGE, Elliptic boundary value problems in corner domains - smoothness and asymptotics of solutions. L.M.N. 1341, Springer-Verlag, (1988). Zbl0668.35001 MR961439 · Zbl 0668.35001 · doi:10.1007/BFb0086682 [2] M. DAUGE, M. S. LUBUMA et S. NICAISE, Coefficients des singularités pour le problème de Dirichlet sur un polygone. C.R. Acad. Sc. Paris, 304 (1987). Zbl0619.35033 MR894574 · Zbl 0619.35033 [3] P. GRISVARD, Elliptic problems in non smooth domains. Monographs and Studies in Math. 24, Pitman (1985). Zbl0695.35060 · Zbl 0695.35060 [4] P. GRISVARD, Problèmes aux limites sur un polygone. Mode d’emploi, E.D.F. Série C n^\circ l, 1986, pp. 21-59 Zbl0623.35031 MR840970 · Zbl 0623.35031 [5] V. A. KONDRATEV, Boundary-value problems for elliptic equations in domains with conical or angular points. Trans. Moscow Math. Soc.16, 227-313 (1967). Zbl0194.13405 MR226187 · Zbl 0194.13405 [6] V. G. MAZ’YA et B. A. PLAMENEVSKII, Coefficients in the asymptotics of the solutions of an elliptic boundary value problem in a cone. A.M.S. Transl. (2) 123, 57-88 (1984). Zbl0554.35036 · Zbl 0554.35036 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.