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We establish two new estimates which control a function (after subtracting its average) in $L^1$ by only the $L^1$ norm of its radial derivative. While the interior estimate holds for all superharmonic functions, the boundary version is…
We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is…
We undertake a semiclassical analysis of the spectral properties (modulations of photoabsorption spectra, energy level statistics) of a simple Rydberg molecule in static fields within the framework of Closed-Orbit/Periodic-Orbit theories.…
Recently, reduced order modeling methods have been applied to solving inverse boundary value problems arising in frequency domain scattering theory. A key step in projection-based reduced order model methods is the use of a sesquilinear…
A major challenge of many diffraction calculations, using some form of the Rayleigh-Sommerfeld formulas, is the integration of a highly oscillatory integrand. Here we derive a potentially useful alternative form of solution to the Helmholtz…
The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of $n-1$ dimensional sets across analysis, geometric measure theory, and PDEs. The present paper surveys…
Classical dimensional analysis is one of the cornerstones of qualitative physics and is also used in the analysis of engineering systems, for example in engineering design. The basic power product relationship in dimensional analysis is…
In this manuscript we deal with existence/uniqueness and regularity issues of suitable weak solutions to nonlocal problems driven by fractional Laplace type operators. Different from previous researches, in our approach we consider gradient…
Four-dimensional spacetime, together with a natural generalisation to extra dimensions, is obtained through an analysis of the structures and symmetries deriving from possible arithmetic expressions for one-dimensional time. On taking the…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
We prove the existence and uniqueness of weak solution of a Neumann boundary problem for an elliptic partial differential equation (PDE for short) with a singular divergence term which can only be understood in a weak sense. A probabilistic…
It is widely believed that quadratic divergences severely restrict natural constructions of particle physics models beyond the standard model (SM). Supersymmetry provides a beautiful solution, but the recent LHC experiments have excluded…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
For partial differential equations (PDEs) that have $n\geq2$ independent variables and a symmetry algebra of dimension at least $n-1$, an explicit algorithmic method is presented for finding all symmetry-invariant conservation laws that…
We consider elliptic systems with superlinear and subcritical boundary conditions and a bifurcation parameter as a multiplicative factor. By combining the rescaling method with degree theory and elliptic regularity theory, we prove the…
Electromagnetic waves propagating in a layered superconductor with arbitrary momentum with respect to the main crystallographic directions display an unavoidable mixing between longitudinal and transverse degrees of freedom. Here we show…
We consider an elliptic problem with nonlinear boundary condition involving nonlinearity with superlinear and subcritical growth at infinity and a bifurcation parameter as a factor. We use re-scaling method, degree theory and continuation…
We study several versions of the alternating direction method of multipliers (ADMM) for solving the convex problem of finding the distance between two ellipsoids and the nonconvex problem of finding the distance between the boundaries of…
In this paper we address the problem of protecting elliptic curve scalar multiplication implementations against side-channel analysis by using the atomicity principle. First of all we reexamine classical assumptions made by scalar…
We derive a grey linear diffusion equation for photons with respect to inertial (or lab-frame) space and time, using asymptotic analysis in 1D planar geometry. The solution of the equation is the comoving radiation energy density. Our…