Geodesic
On Inequalities of the Friedrichs type for Combined Domains
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 146-157

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Integral inequalities of the Friedrichs type for combined domains with plane and cylindrical symmetries are proved. The optimal constants in the right-hand sides of the inequalities are found. These constants depend on physical and geometrical parameters of the domains. Some generalizations of these inequalities to domains of a different shape are considered.
Keywords: a priori estimate, Friedrichs inequality, variational problem. 
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     author = {Viktor K. Andreev},
     title = {On {Inequalities} of the {Friedrichs} type for {Combined} {Domains}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {146--157},
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     number = {2},
     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a2/}
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Viktor K. Andreev. On Inequalities of the Friedrichs type for Combined Domains. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 2, pp. 146-157. http://geodesic.mathdoc.fr/item/JSFU_2009_2_2_a2/