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On the validity of Friedrichs’ inequalities. (English) Zbl 0555.35003
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

##### 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
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