Generalized Dirac Operators on Nonsmooth Manifolds and Maxwell's Equations.
The Banach Envelopes of Besov and Triebel-Lizorkin Spaces and Applications to Partial Differential Equations.
Semilinear Poisson problems in Sobolev-Besov spaces on Lipschitz domains.
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
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...
Riesz transforms associated with the Hodge Laplacian in Lipschitz subdomains of Riemannian manifolds
We prove -bounds for the Riesz transforms associated to the Hodge-Laplacian equipped with absolute and relative boundary conditions in a Lipschitz subdomain of a (smooth) Riemannian manifold for in a certain interval depending on the Lipschitz character of the domain.
On Bojarski's index formula for nonsmooth interfaces.
Boundary integral methods for harmonic differential forms in Lipschitz domains.
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