We study the regularity of the solution of Dirichlet problem of Poisson equations over a bounded domain.A new sufficient condition,uniformly positive reach is introduced.Under the assumption that the closure of the un...We study the regularity of the solution of Dirichlet problem of Poisson equations over a bounded domain.A new sufficient condition,uniformly positive reach is introduced.Under the assumption that the closure of the underlying domain of interest has a uniformly positive reach,the H^2 regularity of the solution of the Poisson equation is established.In particular,this includes all star-shaped domains whose closures are of positive reach,regardless if they are Lipschitz domains or non-Lipschitz domains.Application to the strong solution to the second order elliptic PDE in non-divergence form and the regularity of Helmholtz equations will be presented to demonstrate the usefulness of the new regularity condition.展开更多
基金partially supported by Simons collaboration(Grant No.246211)the National Institutes of Health(Grant No.P20GM104420)+1 种基金partially supported by Simons collaboration(Grant No.280646)the National Science Foundation under the(Grant No.DMS 1521537)
文摘We study the regularity of the solution of Dirichlet problem of Poisson equations over a bounded domain.A new sufficient condition,uniformly positive reach is introduced.Under the assumption that the closure of the underlying domain of interest has a uniformly positive reach,the H^2 regularity of the solution of the Poisson equation is established.In particular,this includes all star-shaped domains whose closures are of positive reach,regardless if they are Lipschitz domains or non-Lipschitz domains.Application to the strong solution to the second order elliptic PDE in non-divergence form and the regularity of Helmholtz equations will be presented to demonstrate the usefulness of the new regularity condition.
