Related papers: G-Convergence, Dirichlet to Neumann maps and invis…

We reexamine the proofs of isospectrality of the counterexample domains to Kac' question `Can one hear the shape of a drum?' from an analytical viewpoint. We reformulate isospectrality in a more abstract setting as the existence of a…

This paper is concerned with the analysis of time-harmonic electromagnetic scattering from plasmonic inclusions in the finite frequency regime beyond the quasi-static approximation. The electric permittivity and magnetic permeability in the…

In this paper we obtain a Carleman approximation theorem for maps from Stein manifolds to Oka manifolds. More precisely, we show that under suitable complex analytic conditions on a totally real set $ M $ of a Stein manifold $X$, every…

Given a conformally transversally anisotropic manifold $(M,g)$, we consider the semilinear elliptic equation $$(-\Delta_{g}+V)u+qu^2=0\quad \text{on $M$}.$$ We show that an a priori unknown smooth function $q$ can be uniquely determined…

In some previous works, the analytic structure of the spectrum of a quantum graph operator as a function of the vertex conditions and other parameters of the graph was established. However, a specific local coordinate chart on the…

Let $G$ be a finite group acting on a connected open Riemann surface $X$ by holomorphic automorphisms and acting on a Euclidean space $\mathbb R^n$ $(n\ge 3)$ by orthogonal transformations. We identify a necessary and sufficient condition…

We prove a Hardy inequality for uniformly elliptic operators subject to Dirichlet or mixed boundary conditions on domains $\Omega$ with piecewiese smooth boundary in arbitrary Riemannian Manifolds (M, g). Employing an approach of E.B.…

We adapt the concept of $\mathcal{K}-$convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions…

We study the inverse problem of identifying a periodic potential perturbation of the Dirichlet Laplacian acting in an infinite cylindrical domain, whose cross section is assumed to be bounded. We prove log-log stable determination of the…

In this work, we give a characterization of Lipschitz operators on spaces of $C^2(M)$ functions (also $C^{1,1}$, $C^{1,\gamma}$, $C^1$, $C^\gamma$) that obey the global comparison property-- i.e. those that preserve the global ordering of…

We prove a sharp criterion on the decay of the tension of almost harmonic maps from degenerating surfaces that ensures that such maps subconverge to a limiting object that is made up entirely of harmonic maps.

Coordinate transformations are a versatile tool to mould the flow of light, enabling a host of astonishing phenomena such as optical cloaking with metamaterials. Moving away from the usual restriction that links isotropic materials with…

We consider the identification of nonlinear diffusion coefficients of the form $a(t,u)$ or $a(u)$ in quasi-linear parabolic and elliptic equations. Uniqueness for this inverse problem is established under very general assumptions using…

We study spectral properties of divergence form elliptic operators $-\textrm{div} [A(z) \nabla f(z)]$ with the Neumann boundary condition in planar domains (including some fractal type domains), that satisfy to the quasihyperbolic boundary…

We prove some uniform and pointwise gradient estimates for the Dirichlet and the Neumann evolution operators $G_{\mathcal{D}}(t,s)$ and $G_{\mathcal{N}}(t,s)$ associated with a class of nonautonomous elliptic operators $\A(t)$ with…

We consider the Laplacian in a domain squeezed between two parallel hypersurfaces in Euclidean spaces of any dimension, subject to Dirichlet boundary conditions on one of the hypersurfaces and Neumann boundary conditions on the other. We…

For $n\ge 3$, let $\Omega$ be a bounded domain in $R^n$ and $N$ be a compact Riemannian manifold in $R^L$ without boundary. Suppose that $u_n\in W^{1,n}(\Omega,N)$ are the Palais-Smale sequences of the Dirichlet $n$-energy functional and…

We consider the Laplacian in a strip $\mathbb{R}\times (0,d)$ with the boundary condition which is Dirichlet except at the segment of a length $2a$ of one of the boundaries where it is switched to Neumann. This operator is known to have a…

Let $(M_i, g_i)_{i \in \mathbb{N}}$ be a sequence of spin manifolds with uniform bounded curvature and diameter that converges to a lower dimensional Riemannian manifold $(B,h)$ in the Gromov-Hausdorff topology. Lott showed that the…

There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or "cloaking") from observation by electromagnetic (EM) waves. Here, we prove invisibility, with respect to solutions of the…