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math.AP2024
A note on the shift theorem for the Laplacian in polygonal domains (extended version)
Jens Markus Melenk, Claudio Rojik
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. T…
math.AP2024
Regularity of vector fields with piecewise regular curl and divergence
Jens Markus Melenk, David Wörgötter
We consider a bounded Lipschitz domain with sufficiently smooth boundary and prove piecewise Sobolev regularity of vector fields that have piecewise regula…