We study a homogeneous parabolic Dirichlet problem involving a possibly degenerate Ornstein-Uhlenbeck operator in a half-space H+ of Rn. We find an explicit formula for the fundamental solution. Under the Hörmander condition of hypoellipticity, we prove a global regularity result in spaces of continuous and bounded functions. We extend our explicit formula to the infinite-dimensional setting.
The fundamental solution for a degenerate parabolic Dirichlet problem.
PRIOLA, Enrico
2000-01-01
Abstract
We study a homogeneous parabolic Dirichlet problem involving a possibly degenerate Ornstein-Uhlenbeck operator in a half-space H+ of Rn. We find an explicit formula for the fundamental solution. Under the Hörmander condition of hypoellipticity, we prove a global regularity result in spaces of continuous and bounded functions. We extend our explicit formula to the infinite-dimensional setting.
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