Abstract An approximation, in the sense of $$\Gamma $$ Γ -convergence and any dimension $$d\ge 1$$ d ≥ 1 , Griffith-type functionals, with p -growth ( $$p>1$$ p > ) symmetrized gradient, is provid...

We introduce a typed programming formalism, type-2 inflationary tiered loop programs or ITLP2, that characterizes the type-2 basic feasible functionals. ITLP2 is based on Bellantoni and Cook’s [BC92] and Leivant’s [Lei95] type-theoretic characterization of polynomial-time and turns out to be closely related to Kapron and Cook’s [KC91, KC96] machine-based characterization of the type-2 basic fea...

Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as h -convex functions. In this paper, we aim to establish functional form of inequalities presented by prove superadditivity monotonicity properties these functionals. Furthermore, de...

In David et al. (Adv Math 350:1109–1192, 2019) and Toro (Regularity of almost minimizers with free boundary. Calculus variations PDEs, 2020), the authors studied for functionals type first by Alt Caffarelli (J Reine Angew 325:105–144, 1981) (Trans Am Soc 282:431–461, 1984). this paper we study regularity to energy variable coefficients (as opposed Caffarelli, J 1981; al., Trans 1984; Adv 2019; ...