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4. Ordinary and Partial Differential Equations, Controlled Differential Systems

Layer potentials on manifolds with cylindrical ends: the Laplace operator

Victor Nistor
Université de Lorraine, Metz, France

Abstract:

We study the method of Layer Potentials on manifolds with cylindrical ends. This includes domains in $\mathbb{R}^n$ with outlets at infinity. One of the main difficulties is the characterization of the Fredholm properties of the resulting integral operators, which requires information on the behavior at infinity. Joint work with Marius Mitrea and Mirela Kohr. We apply our results to the study of the Laplacian. Applications for the Stokes system and further results on the Laplacian will be discussed in the subsequent talk by Mirela Kohr.