AN H s , p ( curl ; Ω ) ESTIMATE FOR THE MAXWELL SYSTEM MANAS KAR AND MOURAD
نویسندگان
چکیده
We derive an H 0 (curl; Ω) estimate for the solutions of the Maxwell type equations modeled with anisotropic and W s,∞(Ω)-regular coefficients. Here, we obtain the regularity of the solutions for the integrability and smoothness indices (p, s) in a plan domain characterized by the apriori lower/upper bounds of a and the apriori upper bound of its Hölder semi-norm of order s. The proof relies on a perturbation argument generalizing Gröger’s L-type estimate, known for the elliptic problems, to the Maxwell system.
منابع مشابه
Reconstruction of interfaces using CGO solutions for the Maxwell equations
We deal with the problem of reconstructing interfaces using complex geometrical optics solutions for the Maxwell system. The contributions are twofold. First, we justify the enclosure method for the impenetrable obstacle case avoiding any assumption on the directions of the phases of the CGO's (or the curvature of obstacle's surface). In addition, we need only a Lipschitz regularity of this sur...
متن کاملOn the inverse elastic scattering by interfaces using one type of scattered waves
We deal with the problem of the linearized and isotropic elastic inverse scattering by interfaces. We prove that the scattered P -parts or S-parts of the far field pattern, corresponding to all the incident plane waves of pressure or shear types, uniquely determine the obstacles for both the penetrable and impenetrable obstacles. In the analysis, we assume only the Lipschitz regularity of the i...
متن کاملReconstruction of Interfaces from the Elastic Farfield Measurements Using CGO Solutions
In this work, we are concerned with the inverse scattering by interfaces for the linearized and isotropic elastic model at a fixed frequency. First, we derive complex geometrical optic solutions with linear or spherical phases having a computable dominant part and an H α-decaying remainder term with α < 3, where H α is the classical Sobolev space. Second, based on these properties, we estimate ...
متن کاملReconstructing Obstacles by the Enclosure Method Using in One Step the Farfield Measurements
In this work, we are concerned with the reconstruction of the obstacles by the enclosure method using the farfield measurements in one step. To justify this, first we state the indicator function of the enclosure method linking directly the farfield pattern to the reflected solutions corresponding to the used complex geometrical optics solutions. Second, we use layer potential techniques to der...
متن کاملGains from diversification on convex combinations: A majorization and stochastic dominance approach
By incorporating both majorization theory and stochastic dominance theory, this paper presents a general theory and a unifying framework for determining the diversification preferences of risk-averse investors and conditions under which they would unanimously judge a particular asset to be superior. In particular, we develop a theory for comparing the preferences of different convex combination...
متن کامل