DIRICHLET - TRANSMISSION PROBLEMS FOR GENERAL BRINKMAN OPERATORS ON LIPSCHITZ AND C-1 DOMAINS IN RIEMANNIAN MANIFOLDS

作者：Kohr Mirela^*; Pintea Cornel; Wendland Wolfgang L

来源：Discrete and Continuous Dynamical Systems-Series B, 2011, 15(4): 999-1018.

DOI：10.3934/dcdsb.2011.15.999

• Brinkman operator
• Stokes operator
• Lipschitz and C-1 domains
• Riemannian manifold
• Dirichlet-transmission problem
• Layer potential operators

In this paper we use a layer potential method to obtain an existence and solvability result in Sobolev spaces for a Dirichlet-transmission problem given in terms of general Brinkman operators, when the solution is defined in two adjacent Lipschitz or C-1 domains on a Riemannian manifold and satisfies prescribed transmission conditions at the interface between these domains, and an additional Dirichlet condition on an external boundary.

• 出版日期2011-6