arXiv subjects
Publications and source records attributed to Kijung Lee.
In this paper second-order elliptic and parabolic partial differential systems are considered on $C^1$ domains. Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solutions to blow up near the boundary. The coefficients of the systems are allowed to substantially oscillate or blow up near the boundary.
In this paper we study the stochastic partial differential systems of divergence type with $C^1$ space domains in $\bR^d$. Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solution to blow up near the boundary. The coefficients of the systems are only measurable and are allowed to blow up near the boundary.
For a superprocess under a stochastic flow, we prove that it has a density with respect to the Lebesgue measure for d=1 and is singular for d>1. For d=1, a stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov's L_p-theory for linear SPDE. A snake representation for this superprocess is established. As applications of this representation, we prove the compact support property for general d and singularity of the process when d>1.