Geodesic
Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface
Mathematica Bohemica, Tome 138 (2013) no. 2, pp. 185-224

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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.
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.
DOI : 10.21136/MB.2013.143291
Classification : 35B65, 35J25
Keywords: elliptic transmission problem; regularity theory; Lipschitz continuity 
Druet, Pierre-Etienne. Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface. Mathematica Bohemica, Tome 138 (2013) no. 2, pp. 185-224. doi: 10.21136/MB.2013.143291
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