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Transmission problems on polygonal networks for systems of PDEs. (Problèmes de transmission sur des réseaux polygonaux pour des systèmes d’EDP.) (French) Zbl 1078.35514

Summary: We study transmission problems for Agmon-Douglis-Nirenberg elliptic systems on polygonal networks with general boundary and interface conditions. We generalize a result from [S. Nicaise and A.-M. Sändig, Math. Methods Appl. Sci. 17, No. 6, 395–429, 431–450 (1994; Zbl 0824.35014, Zbl 0824.35015)] in the two-dimensional case when the operators may be of different order: the solution admits a decomposition into a ‘regular part’ and a finite linear combination of ‘singular’ functions. For some mechanical examples, we give results about the singular exponents and also obtain the regularity of the solution.

MSC:

35J45 Systems of elliptic equations, general (MSC2000)
35B65 Smoothness and regularity of solutions to PDEs
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References:

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