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We investigate the invisibility via anomalous localized resonance of a general source in anisotropic media for electromagnetic waves. To this end, we first introduce the concept of doubly complementary media in the electromagnetic setting. These are media ...
We establish improved versions of the Hardy and Caffarelli-Kohn-Nirenberg inequalities by replacing the standard Dirichlet energy with some nonlocal nonconvex functionals which have been involved in estimates for the topological degree of continuous maps f ...
This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the ...
We present new results concerning the approximation of the total variation, ∫Ω∣∇u∣, of a function u by non-local, non-convex functionals of the form $$ \Lambda_\delta u = \int_{\Omega} \int_{\Omega} \frac{\delta \varphi \big( |u(x) - ...
Using the backstepping approach we recover the null controllability for the heat equations with variable coefficients in space in one dimension and prove that these equations can be stabilized in finite time by means of periodic time-varying feedback laws. ...
Cloaking a source via anomalous localized resonance (ALR) was discovered by Milton and Nicorovici in [15]. A general setting in which cloaking a source via ALR takes place is the setting of doubly complementary media. This was introduced and studied in [20 ...
We present new results concerning the approximation of the total variation, integral(Omega)vertical bar del u vertical bar, of a function u by non-local, non-convex functionals of the form Lambda delta(u) = integral(Omega)integral(Omega)delta phi(vertical ...
Elsevier2017
We prove that a nonlocal functional approximating the standard Dirichlet p-norm fails to decrease under two-point rearrangement. Furthermore, we get other properties related to this functional such as decay and compactness. ...
