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An iff solvability condition for the oblique derivative problem. (English) Zbl 0737.35171
Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau 1990-1991, No.XVIII, 7 p. (1991).
The purpose of this note is to prove the following Theorem: For the oblique derivative problem, condition $$(\psi)$$ is equivalent to solvability. — As a matter of fact, the proof is a modification of the argument we used to handle the two dimensional case of the Nirenberg- Treves conjecture for pseudodifferential operators in [Ann. of Math. 128, 243-258 (1988; Zbl 0682.35112)]. The basic remark is that the oblique derivative problem is equivalent to a pseudodifferential equation of a very particular type $$\partial_ t+\alpha(t,x)\Omega(t,x,D_ x)$$ where $$\Omega$$ is a non-negative pseudodifferential operator and $$\alpha$$ a smooth function.

##### MSC:
 35S15 Boundary value problems for PDEs with pseudodifferential operators 35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
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