There are moments in history, perceived both individually and collectively, in which proposing to imagine—even project—becomes an apparently unattainable task. 2020 took us socially unprepared and, although in some places the current situation is deeply serious while others feel more tolerable, we have a total uncertainty about the future. We can consider that the information that allows us to visualize the indicators leading to situations like the current one is available. However, not all of us have the tools to interpret them, and the voices of those who do have them are not echoed strong enough, unlike those who in spaces of power, political or economic with the means and will to bring fear to wide sectors of the population.
In this paper, we establish higher integrability of the gradient of the solution of the quasilinear elliptic equation $Δ_Au=\text{div}\left(\frac{a(|F|)}{|F|}F\right)$ in $\mathbb{R}^n$, where $Δ_Au$ is the so called A-Laplace operator.
Initial-boundary value problem for the generalized Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. Critical and subcritical powers in nonlinearity are studied.
In this note we consider high energy eigenfunctions of the harmonic oscillator in $\mathbb{R}^d$ and prove that any invariant measure on the energy surface can be written as a weak limit of eigenfunctions.
Existence of mass-conserving self-similar solutions with a sufficiently small total mass is proved for a specific class of homogeneous coagulation and fragmentation coefficients. The proof combines a dynamical approach to construct such solutions for a regularised coagulation-fragmentation equation in scaling variables and a compactness method.
Nodal solutions of a parametric (p_1,p_2)-Laplacian system, with Neumann boundary conditions, are obtained by chiefly constructing appropriate sub-super-solution pairs.
We show that two distinct level sets of the vorticity of a solution to the 2D Euler equations on a disc can approach each other along a curve at an arbitrarily large exponential rate.
While Archaeology started to take form as a professional discipline, Alternative Archaeologies grew in several ways. As the years went by, the image of Archaeology started being corrupted by misconceptions and a lot of imagination, and those professionals that were claiming to be scientists forgot one of their first responsibilities; the public. This lack of interest is one of the reasons why today, a vast majority of society believes in many clichés of the past that alternative archaeologists have used to build a fictitious History that is not innocent at all. From UFOs and the mysteries of great civilizations to the political interpretation of the past, the dangers of Alternative Archaeologies are clear and under our responsibility. This paper analyzes this situation in order to propose a strategy that may make us the main characters of the popular imagery in the mid-term. Since confrontation and communication do not seem to be effective approaches, we need a change in the paradigm based on Public Archaeology and the increase of our presence in everyday life.
The initial value problem for some defocusing coupled nonlinear Schrodinger equations is investigated. Global well-posedness and scattering are established.
In this paper we analyze the dispersion property of some models involving Schrödinger equations. First we focus on the discrete case and then we present some results on graphs.
We study the phenomenon of increasing stability in the diffuse optical tomography (DOT). It is well-known that the DOT inverse problem is exponentially ill-posed. In this paper, we show that the ill-posedness decreases when we increase the frequency.
We prove the unique continuation property for the differential inequality $|(-Δ)^{α/2}u|\leq|V(x)u|$, where $0<α<n$ and $V\in L_{\textrm{loc}}^{n/α,\infty}(\mathbb{R}^n)$, $n\geq3$.
The maximal Orlicz space such that the mixed logarithmic means of multiple Fourier series for the functions from this space converge in $L_{1}$-norm is found.
We improve our previous generalizations to Arsove's and Ko\lodziej's and Thorbiörnson's results concerning the subharmonicity of a function subharmonic with respect to the first variable and harmonic with respect to the second.