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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
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