相关论文: Quantitative Trace Estimates for the Maxwell syste…

In this paper, we consider the isotropic relaxed micromorphic model in polar coordinates and use this representation to solve explicitly an elastostatic axisymmetric extension problem involving a linear system of ordinary differential…

We consider the time-harmonic acoustic wave scattering by a bounded {\it anisotropic inhomogeneity} embedded in an unbounded {\it anisotropic} homogeneous medium. The material parameters may have discontinuities across the interface between…

This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic equation. By analyzing carefully the nonlinear structure of…

We construct a complete conformal scattering theory for finite energy Maxwell potentials on a class of curved, asymptotically flat spacetimes with prescribed smoothness of null infinity and a non-zero ADM mass. In order to define the full…

This article offers a study of the Calder\'on type inverse problem of determining up to second order coefficients of the higher order elliptic operator. Here we show that it is possible to determine an anisotropic second order perturbation…

Including the previously untreated borderline cases, the trace spaces in the distributional sense of the Besov--Lizorkin--Triebel spaces are determined for the anisotropic (or quasi-homogeneous) version of these classes. The ranges of the…

This paper is concerned with the inverse scattering problem for the three-dimensional Maxwell's equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic…

We consider the variational problem of minimizing an anisotropic perimeter functional under a volume constraint in a Euclidean convex domain. We extend to this setting analytical properties of the isoperimetric profile, topological features…

The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…

We develop a minisuperspace formulation of the classical double copy for anisotropic Lifshitz spacetimes in arbitrary dimension. By imposing static symmetries at the level of the action, the gravitational system reduces to an effective…

The present paper proposes and analyzes an interior penalty technique using $C^0$-finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the…

This paper investigates the possible scattering and non-scattering behavior of an anisotropic and inhomogeneous Lipschitz medium at a fixed wave number and with a single incident field. We connect the anisotropic non-scattering problem to a…

In this article, we study the anisotropic Calder\'on problems for the non local logarithimic Schr\"odinger operators $(-\Delta_g+m)\log{(-\Delta_g+m)}+V$ with $m>1$ on a closed, connected, smooth Riemannian manifold of dimension $n\geq2$.…

We establish the $L^p$ resolvent estimates for the Stokes operator in Lipschitz domains in $R^d$, $d\ge 3$ for $|\frac{1}{p}-1/2|< \frac{1}{2d} +\epsilon$. The result, in particular, implies that the Stokes operator in a three-dimensional…

In this paper, we consider a family of Sturm-Liouville operators on the $\omega$-periodic domain. The bifurcation with respect to the parameter region is studied, and the elliptic regions are estimated by trace formula. At last, these…

We study a generalization of the manifold-valued Rudin-Osher-Fatemi (ROF) model, which involves an initial datum $f$ mapping from a curved compact surface with smooth boundary to a complete, connected and smooth $n$-dimensional Riemannian…

We present a method for contraction-based feedback motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset,…

Using a new local smoothing estimate of the first and third authors, we prove local-in-time Strichartz and smoothing estimates without a loss exterior to a large class of polygonal obstacles with arbitrary boundary conditions and…

It is well known that Maxwell equations can be expressed in a unitary Schrodinger-Dirac representation for homogeneous media. However, difficulties arise when considering inhomogeneous media. A Dyson map points to a unitary field qubit…

We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain…