We prove Harnack inequality and global regularity results for weak solutions of quasilinear degenerate equations driven by operators Grushin type with natural growth. Degeneracy is a power strong A_infinity weight. Regularity are achieved under minimal assumptions on the lower order coefficients.

We study the large-time behaviour of Eulerian systems augmented with non-local alignment. Such systems arise as hydrodynamic descriptions of agent-based models for self-organized dynamics, e.g. Cucker & Smale (2007 IEEE Trans. Autom. Control 52, 852-862. (doi:10.1109/TAC.2007.895842)) and Motsch & Tadmor (2011 J. Stat. Phys. 144, 923-947. (doi:10.1007/s10955-011-0285-9)) models. We prove that, ...

In this paper we analyze the three-dimensional Peterlin viscoelastic model. By means of a mixed Galerkin and semigroup approach prove existence weak solutions. Further combining parabolic regularity with relative energy method derive conditional weak-strong uniqueness result.

The strong conical hull intersection property and bounded linear regularity are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. These fundamental notions occur in various branches of convex optimization (constrained approximation, convex feasibility problems, linear inequalities, for instance). It is shown that the standard constraint qualificatio...

In this paper, we introduce a notion of weak pointwise Hölder regularity, starting from the definition of the pointwise anti-Hölder irregularity. Using this concept, a weak spectrum of singularities can be defined as for the usual pointwise Hölder regularity. We build a class of wavelet series satisfying the multifractal formalism and thus show the optimality of the upper bound. We also show th...

Large circuits, whether they are arithmetic, digital signal processing, switching, or processors, typically contain a greater portion of highly regular datapath logic. Datapath synthesis algorithms preserve these regular structures, so they can be exploited by packing, placement, and routing tools for speed or density. Typical datapath synthesis algorithms , however, sacrifice area to gain regu...