16, dim V V U, V U V (c) ϕ P V, p, q ϕ = p/q, q(p ) 0, ϕ P (regular), P ϕ ϕ dom ϕ, ϕ ϕ P ϕ ϕ(p ) = p(p )/q(p ), k (= A 1 ) ϕ(p ) = 0 P ϕ (zero) 1.3, P

In general, Liouville type theorems for stable solutions of nonlinear elliptic equations are usually guaranteed in low dimensional case.. The main purpose of this paper is to obtain

Note that the assumptions of that theorem can be checked with Theorem 2.2 (cf. The stochastic in- tegration theory from [20] holds for the larger class of UMD Banach spaces, but we

The surfaces of degree 3 contained in X are either reducible in the union of three planes and hence linearly equivalent to 3R (when reduced they are the union of three planes meeting

Suppose D is a linear system. On the other hand, by the definition of a system composed with a pencil, the general curve of such a system may have a singular point only at the

In Sections 8.1–8.3, we give some explicit formulas on the Jacobi functions, which are key to the proof of the Parseval–Plancherel-type formula of branching laws of

In addition to the basic facts just stated on existence and uniqueness of solutions for our problems, the analysis of the approximation scheme, based on a minimization of the

The construction of homogeneous statistical solutions in [VF1], [VF2] is based on Galerkin approximations of measures that are supported by divergence free periodic vector fields

p≤x a 2 p log p/p k−1 which is proved in Section 4 using Shimura’s split of the Rankin–Selberg L -function into the ordinary Riemann zeta-function and the sym- metric square