The C^∞-regularity up to the boundary of solutions to the Dirichlet problem: Lu = = f ∈ C^∞ (Ω̄),u|∂Ω = g ∈ C∞ (∂Ω) is proved, using a comparison principle of L with a Hörmander's type operator Σ Xj*Xj, where Ω is a smooth bounded open subset of Rn, and L = - Σi,j ∂i(aij(x)∂j) + c(x) is a second-order degenerate elliptic operator with smooth coefficients, satisfying the so-called Fefferman-Phong's condition.
The Dirichlet problem for sub-elliptic second order equations
A. Parmeggiani;
1997
Abstract
The C^∞-regularity up to the boundary of solutions to the Dirichlet problem: Lu = = f ∈ C^∞ (Ω̄),u|∂Ω = g ∈ C∞ (∂Ω) is proved, using a comparison principle of L with a Hörmander's type operator Σ Xj*Xj, where Ω is a smooth bounded open subset of Rn, and L = - Σi,j ∂i(aij(x)∂j) + c(x) is a second-order degenerate elliptic operator with smooth coefficients, satisfying the so-called Fefferman-Phong's condition.File in questo prodotto:
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