Mathematics – Analysis of PDEs
Scientific paper
1998-09-30
Mathematics
Analysis of PDEs
Scientific paper
10.1016/S0764-4442(98)80107-9
Let $L$ be an infinitely degenerate second-order linear operator defined on a bounded smooth Euclidean domain. Under weaker conditions than those of H\"ormander, 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.
Bell Denis R.
Mohammed Salah E. -A.
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