- Uniqueness and attribute stream for a non strictly convex singular variational drawback(arXiv)
Creator : Jean-Francois Babadjian, Gilles Francfort
Summary : This work addresses the query of uniqueness of the minimizers of a convex however not strictly convex integral useful with linear progress in a two-dimensional setting. The integrand — whose exact type derives straight from the idea of good plasticity — behaves quadratically near the origin and grows linearly as soon as a selected threshold is reached. Thus, in distinction with the one current literature on uniqueness for functionals with linear progress, that’s that which pertains to the generalized least gradient, the integrand is just not a norm. We make use of hyperbolic conservation legal guidelines hidden within the construction of the issue to sort out uniqueness. Our argument strongly depends on the regularity of a vector subject — the Cauchy stress within the terminology of good plasticity — which permits us to outline attribute traces, after which to make use of the tactic of traits. Utilizing the detailed construction of the attribute panorama evidenced in our preliminary examine cite{BF}, we present that this vector subject is definitely steady, save for probably two factors. The completely different behaviors of the power density at zero and at infinity suggest an inequality constraint on the Cauchy stress. Below a barrier kind convexity assumption on the set the place the inequality constraint is saturated, we present that uniqueness holds for pure Dirichlet boundary information, a stronger end result than that of uniqueness for a given hint on the entire boundary since our minimizers can fail to realize the boundary information.
2. Characterizations of strictly convex areas and proximal uniform regular construction(arXiv)
Creator : Abhik Digar, G. Sankara Raju Kosuru
Summary : We offer just a few characterizations of a strictly convex Banach area. Utilizing this we enhance the principle theorem of [Digar, Abhik; Kosuru, G. Sankara Raju; Cyclic uniform Lipschitzian mappings and proximal uniform normal structure. Ann. Funct. Anal. 13 (2022)]
