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Local and global estimates of the derivatives of solutions of inhomogeneous hypoelliptic equations. (English. Russian original) Zbl 0649.35020

Sov. Math., Dokl. 35, No. 3, 570-574 (1987); translation from Dokl. Akad. Nauk SSSR 294, No. 4, 777-781 (1987).
The authors present four theorems on estimates of derivatives of solutions of inhomogeneous hypoelliptic equations \(\Sigma a_{\alpha}(x)D^{\alpha}u(x)=f(x)\) with coefficients \(a_{\alpha}ions\), if \(\Omega\) is not contractible; - this was known e.g. for \(\Omega\) an annulus (and non-existence is known for \(\Omega\) starshaped). Hence this result clarifies the influence of the topology of the domain to the existence problem.
Reviewer: M.Wiegner

MSC:

35H10 Hypoelliptic equations
35B45 A priori estimates in context of PDEs
35E20 General theory of PDEs and systems of PDEs with constant coefficients
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