Đề tài " The resolution of the Nirenberg-Treves conjecture "

Chia sẻ: Nguyen Nhi | Ngày: | Loại File: PDF | Số trang:41

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We give a proof of the Nirenberg-Treves conjecture: that local solvability of principal-type pseudo-diﬀerential operators is equivalent to condition (Ψ). This condition rules out sign changes from − to + of the imaginary part of the principal symbol along the oriented bicharacteristics of the real part. We obtain local solvability by proving a localizable a priori estimate for the adjoint operator with a loss of two derivatives (compared with the elliptic case). The proof involves a new metric in the Weyl (or Beals-Feﬀerman) calculus which makes it possible to reduce to the case when the gradient of the imaginary...

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