This paper presents a system approach to tackle problems involved in automated map generalization. The system combines database generalization and dynamic object generalization capabilities and is coupled with a map agent on top of a map object. The map agent is for the construction of navigating maps, performing tasks on behalf of, and communicating with, users. The object classes are topologi...

We prove local Calderón-Zygmund estimates for weak solutions of the evolutionary p(x, t)-Laplacian system ∂tu− div ( a(x, t)|Du|p(x,t)−2Du ) = div ( |F |p(x,t)−2F ) under the classical hypothesis of logarithmic continuity for the variable exponent p(x, t). More precisely, we show that the spatial gradient Du of the solution is as integrable as the right-hand side F , i.e. |F |p(·) ∈ Lqloc =⇒ |D...

This paper focuses on the operator-theoretic properties (boundedness and compactness) of Hankel operators Fock-Sobolev spaces Fp,m in terms symbols BMO pr VMO spaces, respectively, for a non-negative integers m, 1 ? p < r > 0. Along way, we also study Berezin transform Fp,m. 2020 Mathematics Subject Classification. Primary 47B35; Secondary 30H20, 30H35. Keywords. operators, transform, spa...

We prove the partial Hölder continuity for minimizers of quasiconvex functionals \begin{equation*} \mathcal{F}({\bf u}) \colon =\int_{\Omega} f(x,{\bf u},D{\bf u})\,\textrm{d} x, \end{equation*} where $f$ satisfies a uniform VMO condition with respect to $x$ -variable and is continuous ${\bf u}$ . The growth gradient variable assumed general one.