Křížek, Michal; Neittaanmäki, Pekka On the validity of Friedrichs’ inequalities. (English) Zbl 0555.35003 Math. Scand. 54, 17-26 (1984). Authors’ abstract: A standard proof of Friedrichs’ second inequality \[ \| u\|_{1,\Omega}\leq C(\| div u\|_{0,\Omega}+\| rot u\|_{0,\Omega}) \] is based on contradiction argumentation. In this paper a direct proof is presented. Moreover, necessary and sufficient conditions for the validity of Friedrichs’ first and second inequality are given for plane domains. Reviewer: J.Wloka Cited in 14 Documents MSC: 35B45 A priori estimates in context of PDEs 76W05 Magnetohydrodynamics and electrohydrodynamics 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:magnetohydrodynamics; Friedrichs’ second inequality × Cite Format Result Cite Review PDF Full Text: DOI EuDML