Showing papers by "Marius Mitrea published in 1999"
TL;DR: In this paper, the Laplace operator on Lipschitz domains in a manifold with C 1 metric tensor was treated and the Dirichlet, Neumann, and oblique derivative boundary problems were studied.
163 citations
TL;DR: In this article, a simple, Clifford algebra-based approach to several key results in the theory of Maxwell's equations in non-smooth subdomains of R m is presented.
Abstract: We present a simple, Clifford algebra-based approach to several key results in the theory of Maxwell's equations in non-smooth subdomains of R m . Among other things, we give new proofs to the boundary energy estimates of Rellich type for Maxwell's equations in Lipschitz domains from [20, 10], discuss radiation conditions and the case of variable wave number.
75 citations
15 citations
TL;DR: In this paper, a Dirac type operator on a compact manifold M and Σ being a Lipschitz submanifold of codimension one partitioning M into two Lipschnitz domains Ω± were considered.
Abstract: Let D be a Dirac type operator on a compact manifold M and let Σ be a Lipschitz submanifold of codimension one partitioningM into two Lipschitz domains Ω±. Also, let Hp±(Σ, D) be the traces on Σ of the (Lpstyle) Hardy spaces associated with D in Ω±. Then (Hp−(Σ, D),Hp+(Σ, D)) is a Fredholm pair of subspaces for Lp(Σ) (in Kato’s sense) whose index is the same as the index of the Dirac operator D considered on the whole manifold M.
3 citations
TL;DR: In this article, it was shown that under a small perturbation (in the Euclidean metric) of the boundary of a Lipschitz domain there corresponds a small variation in the uniform norm of the elastic far-field pattern.
Abstract: We prove that under a small perturbation (in the Euclidean metric) of the boundary of a Lipschitz domain there corresponds a small variation (in the uniform norm) of the elastic far-field pattern. The corresponding estimate is of Holder type. This is done under the assumptions that the Lipschitz character of the perturbation is bounded and that the frequency of the elastic waves is either sufficiently small or has a strictly positive imaginary part.