相关论文: Quantitative Trace Estimates for the Maxwell syste…
We establish Strichartz estimates for the Schr\"odinger equation on Riemannian manifolds $(\Omega,\g)$ with boundary, for both the compact case and the case that $\Omega$ is the exterior of a smooth, non-trapping obstacle in Euclidean…
We consider relativistic plasma particles subjected to an external gravitation force in a $3$D half space whose boundary is a perfect conductor. When the mean free path is much bigger than the variation of electromagnetic fields, the…
We study the time-harmonic Maxwell equations on bounded Lipschitz domains with an impedance boundary condition. The impedance coefficient can be matrix valued such that, in particular, a polarization dependent impedance is modeled. We…
In this paper, the main aim is to consider the boundedness of commutators of multilinear Calder\'{o}n-Zygmund operators with Lipschitz functions in the context of the variable exponent Lebesgue spaces. Furthermore, the variable versions of…
We establish large-scale interior Lipschitz estimates for solutions to systems of linear elasticity with rapidly oscillating periodic coefficients and Dirichlet boundary conditions in domains with periodically placed inclusions of size…
In this paper two properties of recognized interest in variational analysis, known as Lipschitz lower semicontinuity and calmness, are studied with reference to a general class of variational systems, i.e. to solution mappings to…
We prove local Strichartz estimates on compact manifolds with boundary. Our results also apply more generally to compact manifolds with Lipschitz metrics.
We provide a novel approach to approximate bounded Lipschitz domains via a sequence of smooth, bounded domains. The flexibility of our method allows either inner or outer approximations of Lipschitz domains which also possess weakly defined…
A well-known result is that any Lipschitz domain is an extension domain for $W^{s,p}$. This paper extends this result to Lipschitz subsets of compact Lipschitz submanifolds of $\mathbb{R}^n$. We adapt the construction of an extension…
We study the quantitative transfer of uniqueness from the classical to the fractional Calder\'on problem with exterior data. This allows us to deduce the first stability estimates for the principal part of the isotropic fractional…
We consider the Calder\`on problem in an infinite cylindrical domain, whose cross section is a bounded domain of the plane. We prove log-log stability in the determination of the isotropic periodic conductivity coefficient from partial…
This paper analyzes the Lipschitz behavior of the feasible set in two parametric settings, associated with linear and convex systems in R^n. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified…
This research develops a well-established analytical solution of the Einstein-Maxwell field equations. We analyze the behavior of a spherically symmetric and static interior driven by a charged anisotropic matter distribution. The class I…
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…
We study the quantitative stability of the mapping that to a measure associates its pushforward measure by a fixed (non-smooth) optimal transport map. We exhibit a tight H\"older-behavior for this operation under minimal assumptions. Our…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
We study extension theorems for Lipschitz-type operators acting on metric spaces and with values on spaces of integrable functions. Pointwise domination is not a natural feature of such spaces, and so almost everywhere inequalities and…
The paper studies properties of acoustic operators in bounded Lipschitz domains $\Omega$ with m-dissipative generalized impedance boundary conditions. We prove that such acoustic operators have a compact resolvent if and only if the…
We study 2-microlocal Besov and Triebel-Lizorkin spaces with variable exponents on special Lipschitz domains. These spaces are as usual defined by restriction of the corresponding spaces on $\R^n$. In this paper we give two intrinsic…
In this paper, based on the method of scalar perturbations, we construct the \textit{anisotropic} charged Lifshitz background perturbatively upto leading order in the anisotropy. We perform our analysis both in the extremal as well as in…