• Media type: Text; Report; E-Book
  • Title: Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface
  • Contributor: Druet, Pierre-Étienne [Author]
  • imprint: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2010
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.1571
  • Keywords: Elliptic transmission problems -- regularity theory -- Lipschitz continuity ; 35J25 ; article ; 35B65
  • Origination:
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  • Description: 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 compatibility condition for the angle of contact of the two surfaces and the boundary data, we prove the existence of square-integrable second derivatives, and the global Lipschitz continuity of the solution. We show that the second weak derivatives remain integrable to a certain power less than two if the compatibility condition is violated.