We prove existence of solutions and study the nonlocal-to-local asymptotics for nonlocal, convective, Cahn-Hilliard equations in case a W^{1,1} convolution kernel under homogeneous Neumann conditions. Any type potential, possibly also double-obstacle or logarithmic type, is included. Additionally, we highlight variants extensions to setting periodic boundary conditions viscosity contributions, ...

Given a one-dimensional formal group of height 2, let E be the Morava E theory spectrum associated to its universal deformation over the Lubin-Tate ring. By computing with moduli spaces of elliptic curves, we give an explicitation for an algebra of Hecke operators acting on E -cohomology. This leads to a vanishing result for Rezk’s logarithmic cohomology operation on the units of E . It identif...

We calculate the quark part of the kernel of the generalized non-forward BFKL equation at non-zero momentum transfer t in the next-to-leading logarithmic approximation. Along with the quark contribution to the gluon Regge trajectory, this part includes pieces coming from the quark-antiquark production and from the quark contribution to the radiative corrections in one-gluon production in the Re...

We derive the DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin |n|. Its analytic continuation to negative |n| in the leading logarithmic approximation allows us to obtain residues of anomalous dimensions γ of twist-2 operator...

We develop local elliptic gradient estimates for a basic nonlinear f-heat equation with logarithmic power nonlinearity and establish pointwise upper bounds on the weighted heat kernel, all in context of manifolds, where metric potential evolve under Perelman-Ricci type flow. For use is made entropy monotonicity arguments ultracontractivity expressed terms optimal constant Sobolev inequality. So...

In this paper we construct a noncommutative residue for the Heisenberg calculus, that is, for the hypoelliptic calculus on Heisenberg man-ifolds, including on CR and contact manifolds. This noncommutative residue as the residual induced on operators of integer orders by the analytic extension of the usual trace to operators of non-integer orders and it agrees with the integral of the density de...

Starting from the general expression for the ground state correlation energy in the adiabatic-connection fluctuation-dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this fa...