Solvability near the characteristic set for a special class of complex vector fields |
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Authors: | Email author" target="_blank">Paulo?L?Dattori da SilvaEmail author Evandro?R?da?Silva |
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Institution: | 1.Departamento de Matemática,Instituto de Ciências Matemáticas e de Computa??o, Universidade de S?o Paulo,S?o Carlos,Brazil |
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Abstract: | This work deals with the solvability near the characteristic set Σ = {0} × S 1 of operators of the form \({L=\partial/\partial t + (x^na(x) + ix^mb(x))\partial/\partial x}\), \({b\not\equiv0}\) and a(0) ≠ 0, defined on \({\Omega_\epsilon=(-\epsilon,\epsilon)\times S^1}\), \({\epsilon >0 }\), where a and b are real-valued smooth functions in \({(-\epsilon,\epsilon)}\) and m ≥ 2n. It is shown that given f belonging to a subspace of finite codimension of \({C^\infty(\Omega_\epsilon)}\) there is a solution \({u\in L^\infty}\) of the equation Lu = f in a neighborhood of Σ; moreover, the L ∞ regularity is sharp. |
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