Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface

Pierre-Etienne Druet

Mathematica Bohemica (2013)

  • Volume: 138, Issue: 2, page 185-224
  • ISSN: 0862-7959

Abstract

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We investigate the regularity of the weak solution to elliptic transmission problems that involve two layered anisotropic materials separated by a boundary intersecting interface. Under a pair of compatibility conditions for the angle of the two surfaces and the boundary data at the contact line, we prove the existence of up to the boundary square-integrable second derivatives, and the global Lipschitz continuity of the solution. If only the weakest, necessary condition is satisfied, we show that the second weak derivatives remain integrable to a certain power less than two.

How to cite

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Druet, Pierre-Etienne. "Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface." Mathematica Bohemica 138.2 (2013): 185-224. <http://eudml.org/doc/252531>.

@article{Druet2013,
abstract = {We investigate the regularity of the weak solution to elliptic transmission problems that involve two layered anisotropic materials separated by a boundary intersecting interface. Under a pair of compatibility conditions for the angle of the two surfaces and the boundary data at the contact line, we prove the existence of up to the boundary square-integrable second derivatives, and the global Lipschitz continuity of the solution. If only the weakest, necessary condition is satisfied, we show that the second weak derivatives remain integrable to a certain power less than two.},
author = {Druet, Pierre-Etienne},
journal = {Mathematica Bohemica},
keywords = {elliptic transmission problem; regularity theory; Lipschitz continuity; elliptic transmission problem; regularity theory; Lipschitz continuity},
language = {eng},
number = {2},
pages = {185-224},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface},
url = {http://eudml.org/doc/252531},
volume = {138},
year = {2013},
}

TY - JOUR
AU - Druet, Pierre-Etienne
TI - Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface
JO - Mathematica Bohemica
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 138
IS - 2
SP - 185
EP - 224
AB - We investigate the regularity of the weak solution to elliptic transmission problems that involve two layered anisotropic materials separated by a boundary intersecting interface. Under a pair of compatibility conditions for the angle of the two surfaces and the boundary data at the contact line, we prove the existence of up to the boundary square-integrable second derivatives, and the global Lipschitz continuity of the solution. If only the weakest, necessary condition is satisfied, we show that the second weak derivatives remain integrable to a certain power less than two.
LA - eng
KW - elliptic transmission problem; regularity theory; Lipschitz continuity; elliptic transmission problem; regularity theory; Lipschitz continuity
UR - http://eudml.org/doc/252531
ER -

References

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