A note on the shift theorem for the Laplacian in polygonal domains

Jens Markus Melenk; Claudio Rojik

Applications of Mathematics (2024)

  • Volume: 69, Issue: 5, page 653-693
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Melenk, Jens Markus, and Rojik, Claudio. "A note on the shift theorem for the Laplacian in polygonal domains." Applications of Mathematics 69.5 (2024): 653-693. <http://eudml.org/doc/299322>.

@article{Melenk2024,
abstract = {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.},
author = {Melenk, Jens Markus, Rojik, Claudio},
journal = {Applications of Mathematics},
keywords = {Besov space; corner domain; corner singularity; Mellin calculus},
language = {eng},
number = {5},
pages = {653-693},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on the shift theorem for the Laplacian in polygonal domains},
url = {http://eudml.org/doc/299322},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Melenk, Jens Markus
AU - Rojik, Claudio
TI - A note on the shift theorem for the Laplacian in polygonal domains
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 5
SP - 653
EP - 693
AB - 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.
LA - eng
KW - Besov space; corner domain; corner singularity; Mellin calculus
UR - http://eudml.org/doc/299322
ER -

References

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