## An elementary proof of local solvability in two dimensions under condition $$(\Psi)$$.(English)Zbl 0763.35115

The author presents a very nice proof of an energy estimate that implies local solvability of a certain pseudo-differential equation.
Specifically, the equation to be considered is $$Pu=f$$, where $$P$$ is a classical pseudo-differential operator in two dimensions, which is of principal type and satisfies condition $$(\Psi)$$ of Nirenberg and Treves. The proof is based on the observation that, in two dimensions, the canonical form for $$P$$ coincides with the Calderon boundary operator for a boundary-value problem that can be inverted by integration.

### MSC:

 35S05 Pseudodifferential operators as generalizations of partial differential operators
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