Solvability near the characteristic set for a special class of complex vector fields
PL Dattori da Silva, ER da Silva - Archiv der Mathematik, 2012 - Springer
Archiv der Mathematik, 2012•Springer
This work deals with the solvability near the characteristic set Σ= 0× S 1 of operators of the
form L= ∂/∂ t+(x^ na (x)+ ix^ mb (x)) ∂/∂ x, b\not\equiv0 and a (0)≠ 0, defined on\Omega_
ϵ=(-ϵ, ϵ) * S^ 1, ϵ> 0, where a and b are real-valued smooth functions in (-ϵ, ϵ) and m≥ 2
n. It is shown that given f belonging to a subspace of finite codimension of C^ ∞ (\Omega_
ϵ) there is a solution u ∈ L^ ∞ of the equation Lu= f in a neighborhood of Σ; moreover, the
L∞ regularity is sharp.
form L= ∂/∂ t+(x^ na (x)+ ix^ mb (x)) ∂/∂ x, b\not\equiv0 and a (0)≠ 0, defined on\Omega_
ϵ=(-ϵ, ϵ) * S^ 1, ϵ> 0, where a and b are real-valued smooth functions in (-ϵ, ϵ) and m≥ 2
n. It is shown that given f belonging to a subspace of finite codimension of C^ ∞ (\Omega_
ϵ) there is a solution u ∈ L^ ∞ of the equation Lu= f in a neighborhood of Σ; moreover, the
L∞ regularity is sharp.
Abstract
This work deals with the solvability near the characteristic set Σ = {0} × S 1 of operators of the form , and a(0) ≠ 0, defined on , , where a and b are real-valued smooth functions in and m ≥ 2n. It is shown that given f belonging to a subspace of finite codimension of there is a solution of the equation Lu = f in a neighborhood of Σ; moreover, the L ∞ regularity is sharp.
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