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This article focuses on Lp-estimates for the square root of elliptic systems of second order in divergence form on a bounded domain. We treat complex bounded measurable coefficients and allow for mixed Dirichlet/Neumann boundary conditions…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
A popular framework for exploring Lorentz violation is the Standard Model Extension. This extension contains a large number of parameters that can be bounded in various experiments. Most studies, however, focus on the fermion or photon…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
A graviton of a nonzero mass and decay width propagates five physical polarizations. The question of interactions of these polarizations is crucial for viability of models of massive/metastable gravity. This question is addressed in the…
There are observations indicating a possible anomalous transparency of intergalactic space (filled with infrared background light) for extragalactic gamma-rays of very high energy (> 100 GeV). The anomaly is usually associated with effects…
The Standard-Model Extension provides a framework to systematically investigate possible violation of the Lorentz symmetry. Concerning gravity, the linearized version was extensively examined. We here cast the first set of experimental…
The remarkable synergy and complementarity between the circular ${\rm e^+ e^-}$ and pp colliders has been extensively discussed. In this short document, we investigate the complementarity between the proposed circular and linear ${\rm e^+…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
The recently introduced problem of extending partial interval representations asks, for an interval graph with some intervals pre-drawn by the input, whether the partial representation can be extended to a representation of the entire…
Extended technicolor theories generate potentially large corrections to the $\Zbb$ vertex. These can be observed in current experiments at LEP.
We look for pointwise bounds on a plurisubharmonic function near its singularity point, given the value of its generalized Lelong number with respect to a plurisubharmonic weight. To this end, an extremal problem is considered. In certain…
We consider systems of parabolic linear equations, subject to Neumann boundary conditions on bounded domains in $\mathbb{R}^d$, that are coupled by a matrix-valued potential $V$, and investigate under which conditions each solution to such…
We use the precision electroweak data at LEP to place bounds on $B$-violating Yukawa couplings, two theoretically appealing examples being provided by $R$-parity--violating supersymmetry and diquarks. The couplings involving the third…
We study the Coulomb chain where particles are restricted to one dimension and experience three-dimensional Coulomb interactions with their nearest and next-to-nearest neighbours. The distances between consecutive particles are treated as…
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We show an existence of a weak solution of a degenerate and/or singular semilinear elliptic boundary value (nonhomogeneous) problem lying between a given weak subsolution and a given weak supersolution. It has been applied for an existence…
We consider the linearised vacuum Einstein equations around a Kerr exterior solution and present a scheme to prove elliptic $L^2(\mathbb{S}^2)$-estimates for the linearised curvature quantities in the equations. The scheme employs the…
Boundary value problems for the nonlinear Schrodinger equation on the half line in laboratory coordinates are considered. A class of boundary conditions that lead to linearizable problems is identified by introducing appropriate extensions…
We study the equational theory of the Weihrauch lattice with multiplication, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the product $\times$, and the finite…