We study the oblique derivative problem for uniformly elliptic equations on cone domains. Under assumption of axi-symmetry solution, we find sufficient conditions angle vector Hölder regularity gradient to hold up vertex cone. The proof is based application carefully constructed barrier methods or via perturbative arguments. In case that such does not hold, give explicit counterexamples. also a...

We describe how parton recombination can address the recent measurement of dynam-ical jet-like two particle correlations. In addition we discuss the possible effect realistic light-cone wave-functions including higher Fock-states may have on the well-known elliptic flow valence-quark number scaling law.

We study the structure and asymptotic behavior of the resolvent of elliptic cone pseudodifferential operators acting on weighted Sobolev spaces over a compact manifold with boundary. We obtain an asymptotic expansion of the resolvent as the spectral parameter tends to infinity, and use it to derive corresponding heat trace and zeta function expansions as well as an analytic index formula.

We study the geometry of the set of closed extensions of index 0 of an elliptic differential cone operator and its model operator in connection with the spectra of the extensions, and give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.

In this article, we show the existence of multiple positive solutions to a class of degenerate elliptic equations involving critical cone Sobolev exponent and sign-changing weight function on singular manifolds with the help of category theory and the Nehari manifold method.

The purpose of this paper is to study Seshadri constants on the self-product E × E of an elliptic curve E. We provide explicit formulas for computing the Seshadri constants of all ample line bundles on the surfaces considered. As an application, we obtain a good picture of the behaviour of the Seshadri function on the nef cone.

In this paper we prove some existence and regularity results concerning parabolic equations ut = F (x,∇u, D u) + f(x, t) with some boundary conditions, on Ω×]0, T [, where Ω is some bounded domain which possesses the exterior cone property and F is some fully nonlinear elliptic operator, singular or degenerate.

We prove extensions of the estimates of Aleksandrov and Bakel′man for linear elliptic operators in Euclidean space R to inhomogeneous terms in L spaces for q < n. Our estimates depend on restrictions on the ellipticity of the operators determined by certain subcones of the positive cone. We also consider some applications to local pointwise and L estimates.

We prove that the index formula for b-elliptic cone differential operators given by Lesch in [6] holds verbatim for operators whose coefficients are not necessarily independent of the normal variable near the boundary. We also show that, for index purposes, the operators can always be considered on weighted Sobolev spaces.

In this paper, we consider a certain class of discrete pseudo-differential operators in a sharp convex cone and describe their invertibility conditions in L2-spaces. For this purpose we introduce a concept of periodic wave factorization for elliptic symbol and show its applicability for the studying. Key–Words: Discrete operator, Multidimensional periodic Riemann problem, Periodic wave factoriz...