A New H 2 Regularity Condition of the Solution to Dirichlet Problem of the Poisson Equation and Its Applications.
Acta Math Sin Engl Ser
; 36(1): 21-39, 2020 Jan.
Article
em En
| MEDLINE
| ID: mdl-33603567
ABSTRACT
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.
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MEDLINE
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En
Ano de publicação:
2020
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Article