The optimal constant for the trace inequality in BV is explicitly computed for domains with a particular class of singularities.
Giusti , Boundary value problems for non-parametric surfaces of prescribed mean curvature , Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 3 (1976), pp
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Optimal constant for the trace inequality in $BV$ for domains with corners
The optimal constant for the trace inequality in BV is explicitly computed for domains with a particular class of singularities.