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Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains.

Martin DindosMarius Mitrea — 2002

Publicacions Matemàtiques

Extending recent work for the linear Poisson problem for the Laplacian in the framework of Sobolev-Besov spaces on Lipschitz domains by Jerison and Kenig [16], Fabes, Mendez and Mitrea [9], and Mitrea and Taylor [30], here we take up the task of developing a similar sharp theory for semilinear problems of the type Δu - N(x,u) = F(x), equipped with Dirichlet and Neumann boundary conditions.

Boundary value problems and layer potentials on manifolds with cylindrical ends

Marius MitreaVictor Nistor — 2007

Czechoslovak Mathematical Journal

We study the method of layer potentials for manifolds with boundary and cylindrical ends. The fact that the boundary is non-compact prevents us from using the standard characterization of Fredholm or compact pseudo-differential operators between Sobolev spaces, as, for example, in the works of Fabes-Jodeit-Lewis and Kral-Wedland . We first study the layer potentials depending on a parameter on compact manifolds. This then yields the invertibility of the relevant boundary integral operators in the...

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