In this work we consider refined geometric characterizations of mappings generate composition operators on Sobolev spaces. The detailed proofs in the cases $n-1<q<n$ and $n>q$ are given.
We investigate the maximum principle for the weak solutions to the Cauchy problem for the hyperbolic fourth-order linear equations with constant complex coefficients in the plane bounded domain
Ruggeri's hyperbolic Navier-Stokes equations are shown to possess, for any equilibrium state, smooth solutions in arbitrarily small $L^\infty$ neigborhoods of the reference state that in finite time cease to be differentiable.
In an inviscid and incompressible fluid in dimension 3, we prove the existence of several helical filaments, or vortex helices, collapsing into each others.
It must have been around ten years ago, when I was invited to present my -shaky then but promising- progress of PhD thesis at the University of Athens, on social and economic trends in heritage management, discussing island cultural resources and the role of the interested communities. I remember myself at the end of my talk, standing in front of a bewildered and intrigued (in equal doses) audience, only to experience the -somehow- apologetic comment of the organising professor to the audience: “I see that we need to look into these things now, that all became science”. I have talked about this memory elsewhere in detail (Lekakis 2015) mainly to pinpoint that even though 40 years of concrete bibliography have then lapsed -McGimsey, for example, produced his seminal volume in 1972- there was still a lack of information about the concept and practices of public archaeology, at least in the Greek academic context.
We consider the Nemytskii operators $u\to |u|$ and $u\to u^{\pm}$ in a bounded domain $Ω$ with $C^2$ boundary. We give elementary proofs of the boundedness in $H^s(Ω)$ with $0\le s<3/2$.
Large deviation principle by the weak convergence approach is established for the stochastic nonlinear Schrodinger equation in one-dimension and as an application the exit problem is investigated.
In recent years archaeologists have asserted the value of social media for achieving goals such as ‘shared authority’ and the ‘empowerment’ of various communities. These assertions often resemble techno-utopian discourse. However, it is essential to critically consider these assertions with reference to the important studies emerging from the fields of new media studies and Indigenous and collaborative archaeology, which have particularly emphasised the need for a greater awareness of sociopolitical contexts. Informed by this literature, this paper surveys some of the emerging and established uses of social media by archaeologists and museums, and proceeds to introduce factors that challenge the broadly positive discourses about the impact of social media on various communities. It also highlights the need for short- and long-term impact studies.
In post-modernity, the millenarian search for mythical sites has become a tourist attraction and the process of culturalization of consumption has created and is creating a new global heritage. Places already celebrated for leisure have been reinvented as mythical and archaeological sites. A good example is the Atlantis Hotel on Paradise Island, in the Bahamas. Here, Plato’s mythical Atlantis has inspired an underwater pseudo-archaeological reconstruction of a civilization that most likely had never existed. The myth-making force of the sea transforms the false ruins and affects how they are perceived. This is quite consistent with a tourism where authenticity has lost its traditional value and sensory gratifications have replaced it. A more recent Atlantis Hotel in Dubai and another one under construction in China show the vitality of this myth and the strength of the thematization of consumption. Other examples confirm this tendency in even more grotesque ways. At the core of this process there is the body: the tourist’s and the consumer’s body. The post-modernity has enhanced its use as tool and icon of consumption.
Optimal extinction rates near the extinction time are derived for non-negative solutions to a fast diffusion equation with strong absorption, the power of the absorption exceeding that of the diffusion.
We prove unique existence of mild solutions on $L^{\infty}_σ$ for the Navier-Stokes equations in an exterior domain in $ \mathbb{R}^{n}$, $n\geq 2$, subject to the non-slip boundary condition.
We provide a simple proof of a result, due to G. Alberti, concerning a rank-one property for the singular part of the derivative of vector-valued functions of bounded variation.
The time derivative (in the sense of distributions) of the solutions to the Evolutionary p-Laplace Equation is proved to be a function in a local Lebesgue space.