Geodesic
A note on the shift theorem for the Laplacian in polygonal domains
Applications of Mathematics, Tome 69 (2024) no. 5, pp. 653-693 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. The range in which the shift theorem holds depends on the angle of the cone. For the right endpoint of the range, the shift theorem is described in terms of Besov spaces rather than Sobolev spaces.
We present a shift theorem for solutions of the Poisson equation in a finite planar cone (and hence also on plane polygons) for Dirichlet, Neumann, and mixed boundary conditions. The range in which the shift theorem holds depends on the angle of the cone. For the right endpoint of the range, the shift theorem is described in terms of Besov spaces rather than Sobolev spaces.
DOI : 10.21136/AM.2024.0049-24
Classification : 35B65, 35J25
Keywords: Besov space; corner domain; corner singularity; Mellin calculus 
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Melenk, Jens Markus; Rojik, Claudio. A note on the shift theorem for the Laplacian in polygonal domains. Applications of Mathematics, Tome 69 (2024) no. 5, pp. 653-693. doi: 10.21136/AM.2024.0049-24

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