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In this paper we prove the Lipschitz regularity for local minimizers of convex variational integrals of the form F (v , Ω) = ∫ Ω F (x , D v (x)) d x , where, for n ≥ 2 and N ≥ 1 , Ω is a bounded open set in R n , u ∈ W 1 , 1 (Ω , R N) and the energy density F : Ω × R N × n → R satisfies the so called variable growth conditions. The main novelty here is that we assume an almost critical regularity in the Orlicz Sobolev setting for the energy density as a function of the x variable. [ABSTRACT FROM AUTHOR]

Abstract: We deal in detail with the question of existence, uniqueness and asymptotic behaviour of solutions to a parabolic equation with hysteresis and convection. This equation is part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates. The result of this paper complements the content of a previous paper of the first author, where existence of the solution has been proved under fairly general assumptions on the hysteresis operator and the uniqueness was only obtained for a restricted class of hysteresis operators. [Copyright &y& Elsevier]

Abstract: We consider an evolutionary PDE motivated by models for electromagnetic processes in ferromagnetic materials. Magnetic hysteresis is represented by means of a hysteresis operator. Under suitable assumptions, an existence and uniqueness theorem is obtained, together with the Lipschitz continuous dependence on the data and some further regularity results. The discussion of the behaviour of the solution in dependence on physical parameters of the problem is also outlined. [Copyright &y& Elsevier]

We study the Γ -convergence of the functionals F n (u) : = | | f (⋅ , u (⋅) , D u (⋅)) | | p n (⋅) and F n (u) : = ∫ Ω 1 p n (x) f p n (x) (x , u (x) , D u (x)) d x defined on X ∈ { L 1 (Ω , R d) , L ∞ (Ω , R d) , C (Ω , R d) } (endowed with their usual norms) with effective domain the Sobolev space W 1 , p n (⋅) (Ω , R d). Here Ω ⊆ R N is a bounded open set, N , d ≥ 1 and the measurable functions p n : Ω → [ 1 , + ∞) satisfy the conditions ess sup Ω p n ≤ β ess inf Ω p n < + ∞ for a fixed constant β > 1 and ess inf Ω p n → + ∞ as n → + ∞. We show that when f (x , u , ⋅) is level convex and lower semicontinuous and it satisfies a uniform growth condition from below, then, as n → ∞ , the sequence (F n) n Γ -converges in X to the functional F represented as F (u) = | | f (⋅ , u (⋅) , D u (⋅)) | | ∞ on the effective domain W 1 , ∞ (Ω , R d). Moreover we show that the Γ - lim n F n is given by the functional F (u) : = 0 i f | | f (⋅ , u (⋅) , D u (⋅)) | | ∞ ≤ 1 , + ∞ o t h e r w i s e i n X. [ABSTRACT FROM AUTHOR]

In this paper we prove the higher differentiability in the scale of Besov spaces of the solutions to a class of obstacle problems of the type min ∫ Ω F (x , z , D z) : z ∈ K ψ (Ω) . Here Ω is an open bounded set of R n , n ≥ 2 , ψ is a fixed function called obstacle and K ψ (Ω) is set of admissible functions z ∈ W 1 , p (Ω) such that z ≥ ψ a.e. in Ω. We assume that the gradient of the obstacle belongs to a suitable Besov space. The main novelty here is that we are not assuming any differentiability on the partial maps x ↦ F (x , z , D z) and z ↦ F (x , z , D z) , but only their Hölder continuity. [ABSTRACT FROM AUTHOR]

To date, Proteolysis Targeting Chimera (PROTAC) technology has been successfully applied to mediate proteasomal-induced degradation of several pharmaceutical targets mainly related to oncology, immune disorders, and neurodegenerative diseases. On the other hand, its exploitation in the field of antiviral drug discovery is still in its infancy. Recently, we described two indomethacin (INM)-based PROTACs displaying broad-spectrum antiviral activity against coronaviruses. Here, we report the design, synthesis, and characterization of a novel series of INM-based PROTACs that recruit either Von-Hippel Lindau (VHL) or cereblon (CRBN) E3 ligases. The panel of INM-based PROTACs was also enlarged by varying the linker moiety. The antiviral activity resulted very susceptible to this modification, particularly for PROTACs hijacking VHL as E3 ligase, with one piperazine-based compound (PROTAC 6) showing potent anti-SARS-CoV-2 activity in infected human lung cells. Interestingly, degradation assays in both uninfected and virus-infected cells with the most promising PROTACs emerged so far (PROTACs 5 and 6) demonstrated that INM-PROTACs do not degrade human PGES-2 protein, as initially hypothesized, but induce the concentration-dependent degradation of SARS-CoV-2 main protease (Mpro) both in Mpro-transfected and in SARS-CoV-2-infected cells. Importantly, thanks to the target degradation, INM-PROTACs exhibited a considerable enhancement in antiviral activity with respect to indomethacin, with EC 50 values in the low-micromolar/nanomolar range. Finally, kinetic solubility as well as metabolic and chemical stability were measured for PROTACs 5 and 6. Altogether, the identification of INM-based PROTACs as the first class of SARS-CoV-2 Mpro degraders demonstrating activity also in SARS-CoV-2-infected cells represents a significant advance in the development of effective, broad-spectrum anti-coronavirus strategies. [Display omitted] • Exploitation of PROTAC technology on indomethacin led to potent anti-CoVs agents. • A new INM-based PROTAC 6 with potent pan-CoV inhibitory activity was identified. • PROTAC 6 inhibits SARS-CoV-2 in a human cell line in the nanomolar range. • PROTACs 5 and 6 are the first class of SARS-CoV-2 Mpro degraders. • PROTACs 5 and 6 exhibited good chemical and metabolic stability. [ABSTRACT FROM AUTHOR]

Abstract: We propose a temperature dependent model for fatigue accumulation in an oscillating elastoplastic plate. The full system consists of the momentum and energy balance equations, and an evolution equation for the fatigue rate. The main modeling hypothesis is that the fatigue rate is proportional to the dissipation rate. In nontrivial cases, the process develops a singularity (material failure) in finite time. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the determination of the equivalent anisotropy properties of polycrystalline magnetic materials, modelled by an assembly of monocrystalline grains with a stochastic spatial distribution of easy axes. The mathematical theory of is applied to homogenize the anisotropic term in the Gibbs free energy. The procedure is validated focusing on the micromagnetic computation of reversal processes in polycrystalline magnetic thin films. [Copyright &y& Elsevier]

Two years after its emergence, SARS-CoV-2 still represents a serious and global threat to human health. Antiviral drug development usually takes a long time and, to increase the chances of success, chemical variability of hit compounds represents a valuable source for the discovery of new antivirals. In this work, we applied a platform of variably oriented virtual screening campaigns to seek for novel chemical scaffolds for SARS-CoV-2 main protease (Mpro) inhibitors. The study on the resulting 30 best hits led to the identification of a series of structurally unrelated Mpro inhibitors. Some of them exhibited antiviral activity in the low micromolar range against SARS-CoV-2 and other human coronaviruses (HCoVs) in different cell lines. Time-of-addition experiments demonstrated an antiviral effect during the viral replication cycle at a time frame consistent with the inhibition of SARS-CoV-2 Mpro activity. As a proof-of-concept, to validate the pharmaceutical potential of the selected hits against SARS-CoV-2, we rationally optimized one of the hit compounds and obtained two potent SARS-CoV-2 inhibitors with increased activity against Mpro both in vitro and in a cellular context, as well as against SARS-CoV-2 replication in infected cells. This study significantly contributes to the expansion of the chemical variability of SARS-CoV-2 Mpro inhibitors and provides new scaffolds to be exploited for pan-coronavirus antiviral drug development. [Display omitted] • Different virtual screenings led to 30 hits as possible SARS-CoV-2 inhibitors. • Seven inhibitors of SARS-CoV-2 main protease (Mpro) were identified. • These Mpro inhibitors are endowed with novel scaffolds. • Six hit compounds showed antiviral activity against SARS-CoV-2 and other human CoVs. • Rational optimization of hit 7 led to promising Mpro inhibitors, as 36 and 37. [ABSTRACT FROM AUTHOR]