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The Dirichlet problem for superdegenerate differential operators

Denis R. Bell·Salah E. -A. Mohammed
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Abstract

Let $L$ be an infinitely degenerate second-order linear operator defined on a bounded smooth Euclidean domain. Under weaker conditions than those of Hörmander, we show that the Dirichlet problem associated with $L$ has a unique smooth classical solution. The proof uses the Malliavin calculus. At present, there appears to be no proof of this result using classical analytic techniques.

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Denis R. Bell, Salah E. -A. Mohammed. 1998-09-30. The Dirichlet problem for superdegenerate differential operators. https://doi.org/10.1016/s0764-4442(98)80107-9

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