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; ...

The system of Gegenbauer or ultraspherical polynomials $Cn (x);n50,1,.. .% is a classical family of polynomials orthogonal with respect to the weight function vl(x)5(12x ) on the support interval @21,11# . Integral functionals of Gegenbauer polynomials with integrand f (x)@Cn (x)#vl(x), where f (x) is an arbitrary function which does not depend on n or l, are considered in this paper. First, a ...

Given a Hilbert space (H, 〈·, ·〉), and interval Λ ⊂ (0, +∞) and a map K ∈ C(H,R) whose gradient is a compact mapping, we consider the family of functionals of the type: I(λ, u) = 1 2 〈u, u〉 − λK(u), (λ, u) ∈ Λ×H. As already observed by many authors, for the functionals we are dealing with the (PS) condition may fail under just this assumptions. Nevertheless, by using a recent deformation Lemma ...

ABSTRACT. Free Meixner states are a class of functionals on non-commutative polynomials introduced in [Ans06]. They are characterized by a resolvent-type form for the generating function of their orthogonal polynomials, by a recursion relation for those polynomials, or by a second-order non-commutative differential equation satisfied by their free cumulant functional. In this paper, we construc...

In this study, on the subject of harmonic convex functions, we introduce some new functionals linked with weighted integral inequalities for functions. addition, certain Fejér type are discovered.

Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it therefore further explored this paper. In manuscript, we utilize functionals combined with Laplace transform to qualitatively analyze solutions of equation addition, extend our method nonlinear equations infinite delay, several kernels. We menti...

Following recent interest in the qualitative analysis of some optimal control and shape optimisation problems, we provide this article a detailed study Robin boundary conditions PDE constrained calculus variations. Our main model consists an elliptic form −∆u β = f (x, u β) endowed with ∂ν +β(x)u 0. The variable is function β, which assumed to take values between 0 1 have fixed integral. Two ty...

The adsorption of small molecules such as NO or CO on surfaces of magnetic oxides containing transition metals is difficult to model by current density functional approximations. Two such oxides are NiO(100) and Ni-doped MgO(100). Here we compare the results of a theoretical model of the Ni-doped MgO(100) surface with experimental results on NiO(100), which introduces some uncertainty into a qu...