Cutting the loss of derivatives for solvability under condition (psi)

Details Cutting the loss of derivatives for solvability under condition (psi) Cutting the loss of derivatives for solvability under condition (psi)

2005-12-20

arxiv.org/abs/math/0512455v1

Mathematics

Analysis of PDEs

Scientific paper

For a principal type pseudodifferential operator, we prove that condition (psi) implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker's paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from 2 (Dencker's result) to 3/2 (the present paper). It is already known that condition (psi) does not imply local solvability with a loss of 1 derivative, so we have to content ourselves with a loss >1.

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