On the Dirichlet problem for variational integrals in BV

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On the Regularity of Minima of Non-autonomous Functionals (2019, methodology): “tandard (p,q)-case when focusing on this situation (see Remark 6.2 below). The one (1.25)4 is known as µ-ellipticity condition and it is of common use in problems with linear and nearly-linear growth [6,9,27]. It has been introduced in [35]. Remark 1.3. The technique considered here can be modiﬁed u”
Partial Regularity for BV Minimizers (2018, background): “y,and it cannotwork for quasiconvexintegrands. Further referenceson various interesting aspects of existence and regularity of minimizers in the BV context with a standard convexityassumption include [12, 14, 15, 36]. Remark1.2. The mainpointof Theorem1.1is that thesmallness condition(1.8) underthe ”
Regularity of minimizers under limit growth conditions (2017, unknown): “Because of the lack of coercivity we consider the relaxed functional in the class of bounded variation functions BV (Ω), see Theorem 2.7; see also [3] for related results.”