We show that the Markov semigroups generated by a large class of singular stochastic PDEs satisfy the strong Feller property. These include for example the KPZ equation and the dynamical Φ3 model. As a corollary, we prove that the Brownian bridge measure is the unique invariant measure for the KPZ equation with periodic boundary conditions.

We consider T-periodic solutions of singular Hamiltonian systems with weak force q + VV(q,t) = 0, where V(q, t) ~ -l/\q\a near q = 0 with a e (0, 2). In particular, we study some properties of generalized T-periodic solutions, which were introduced by Bahri and Rabinowitz. 0. Introduction In this paper we study properties of the generalized solutions of singular Hamiltonian systems which were i...

We study the boundedness of the Hausdorff measure of the singular set of any solution for a semi-linear elliptic equation in general dimensional Euclidean space Rn. In our previous paper, we have clarified the structures of the nodal set and singular set of a solution for the semi-linear elliptic equation. In particular, we showed that the singular set is (n − 2)-rectifiable. In this paper, we ...

using the group inverse, an explicit solution to a symmetric singular system is described. The general explicit solution is derived when the symmetric singular system satisfies the regularity condition. Certain special properties of these singular systems are presented. Finally, a symmetric balanced realization is obtained from an equivalent standard control system. @ 2002 Elsevier Science Ltd....

In this paper, an improved CBFM/p-FFT algorithm is presented, which can be applied to solve electromagnetic scattering problems of large-scale periodic composite metallic/dielectric arrays, even when the array has electrically small periodicity or separating distance. Using characteristic basis function method (CBFM), scattering characteristics of any inhomogeneous targets can be represented by...

We consider, for p ∈ (1, 2) and q > 1, the p-Laplacian evolution equation with absorption ut = div (|∇u|p−2∇u)− u in R × (0,∞). We are interested in those solutions, which we call singular solutions, that are non-negative, non-trivial, continuous in Rn × [0,∞) \ {(0, 0)}, and satisfy u(x, 0) = 0 for all x = 0. We prove the following: (i) When q ≥ p− 1 + p/n, there does not exist any such singul...

In the case of barotropic FRW cosmologies, the Hubble parameter in conformal time is the solution of a simple Riccati equation of constant coefficients. We consider these cosmologies in the framework of nonrelativistic supersymmetry that has been effective in the area of supersymmetric quantum mechanics. Recalling that Faraoni [Amer. J. Phys. 67 (1999), 732–734] showed how to reduce the barotro...