Burenkov, V. I.; Maman, K. R. 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 Keywords:estimates of derivatives of solutions; inhomogeneous hypoelliptic equations; topology of the domain PDFBibTeX XMLCite \textit{V. I. Burenkov} and \textit{K. R. Maman}, Sov. Math., Dokl. 35, No. 3, 570--574 (1987; Zbl 0649.35020); translation from Dokl. Akad. Nauk SSSR 294, No. 4, 777--781 (1987)