Kapitanskij, L. V.; Piletskas, K. I. On some problems of vector analysis. (Russian. English summary) Zbl 0557.35012 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 138, 65-85 (1984). Summary: We give an explicit method for the construction of a vector field \(\vec v\) in a domain \(\Omega \subset {\mathbb{R}}^ m\), \(m\geq 2\) which has the prescribed divergence \(f=div \vec v\) and boundary values \({\vec \alpha}=\vec v| \partial \Omega\). The differentiability properties of \(\vec v\) are determined in a ”proper way” by the smoothness of f,\({\vec \alpha}\) and \(\partial \Omega\). As a by-product of our construction we obtain the solutions for some other problems of vector analysis which are of self-dependent interest. Cited in 1 ReviewCited in 10 Documents MSC: 35F15 Boundary value problems for linear first-order PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:construction; vector field; prescribed divergence × Cite Format Result Cite Review PDF Full Text: EuDML