Maghnouji, Abderrahman; Nicaise, Serge On a coupled problem between the plate equation and the membrane equation on polygons. (English) Zbl 0794.35046 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 1, No. 2, 187-209 (1992). Summary: We study an interface problem on polygonal domains of the plane, where on one face we consider the biharmonic operator Wikipedia Wikipedia Wolfram MathWorld Wolfram MathWorld and on the other one the Laplace operator Encyclopedia of Mathematics nLab Wikipedia Wolfram MathWorld . We investigate if the associated operator on appropriate Hilbert spaces is a Fredholm operator Encyclopedia of Mathematics nLab Wikipedia or not. If it is, we give an expansion of the variational solution into regular and singular parts. Cited in 1 Document MSC: 35J55 Systems of elliptic equations, boundary value problems (MSC2000) 74K20 Plates 35A20 Analyticity in context of PDEs 35J50 Variational methods for elliptic systems Keywords:interface problem; polygonal domains; biharmonic operator; Laplace operator; expansion of the variational solution into regular and singular parts × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML Geodesic References: [1] Blum, H.) and Rannacher, R.) .- On the boundary value problem of the biharmonic operator on domains with angular corners, Math. Meth. in the Appl. Sc., 2 (1980) pp. 556-581. · Zbl 0445.35023 [2] Dauge, M.) .- Elliptic boundary value problems in corner domains. Smoothness and asymptotics of solutions, , 1341, Springer-Verlag (1988). · Zbl 0668.35001 [3] Dauge, M.) and Nicaise, S.) . - Oblique derivative and interface problems on polygonal domains and networks, Comm. in P.D.E., 14 (1989) pp. 1147-1192. · Zbl 0727.35037 [4] Grisvard, P.) . - Elliptic problems in nonsmooth domains, Monographs and Studies in Mathematics21, Pitman, Boston (1985). · Zbl 0695.35060 [5] Kato, T.) .- Perturbation theory for linear operators, Springer-Verlag (1966). · Zbl 0148.12601 [6] Kondratiev, V.A.) . - Boundary value problems for elliptic equations in domains with conical or angular points, Trans. Moscow Math. Soc., 16 (1967) pp. 227-313. · Zbl 0194.13405 [7] MAZ’YA, V.G. ) andPlamenevskii, B.A.) .- Estimates in Lp and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary, A.M.S. Trans. (2), 123 ( 1984) pp. 1-56. · Zbl 0554.35035 [8] Nečas, J.) . - Les méthodes directes en théorie des équations elliptiques, Masson, Paris (1967). · Zbl 1225.35003 [9] Nicaise, S.) .- Problèmes aux limites sur les réseaux deux dimensionnels polygonaux topologiques, J. Math. Pures et Appl., 67 (1988) pp. 93-103. · Zbl 0698.35047 [10] Nicaise, S.) . - Polygonal interface problems - Higher regularity results, Comm. in P.D.E., 15 (1990) pp. 1475-1508. · Zbl 0731.35030 [11] Nicaise, S.) .- Differential equations in Hilbert spaces and applications to boundary value problems in nonsmooth domains, Journ. of Functional Analysis, 96 (1991) pp. 195-218. · Zbl 0725.34066 [12] Nicaise, S.) . - Polygonal interface problems for the biharmonic operator, Pub. IRMA, Lille, 23, n° XI (1991). · Zbl 0731.35030 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.