Higher regularity of solutions to the singular p-Laplacean parabolic system

We study existence and regularity properties of solutions to the singular $p$-Laplacean parabolic system in a bounded domain $\Omega$. The main purpose is to prove global $L^r(\varepsilon,T;L^q(\Omega))$, $\varepsilon\geq0$, integrability properties of the second spatial derivatives and of the time derivative of the solutions. Hence, for suitable $p$ and exponents $r,\,q$, by Sobolev embedding theorems, we deduce global regularity of $u$ and $\nabla u$ in H\"older spaces. Finally we prove a global pointwise bound for the solution under the assumption $p>\frac{2n}{n+2}$

On the spatial asymptotic decay of a suitable weak solution to the Navier-Stokes Cauchy problem

We prove space-time decay estimates of suitable weak solutions to the Navier-Stokes Cauchy problem, corresponding to a given asymptotic behavior of the initial data of the same order of decay. We use two main tools. The first is a result obtained by the authors in the paper "A remark on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem" (submitted), on the behavior of the solution in a neighborhood of $t=0$ in the $L^\infty_{loc}$-norm, which enables us to furnish a representation formula for a suitable weak solution. The second is the asymptotic behavior of the $L^2(\R^3\setminus B_R)$ norm of $u(t)$ for $R\to\infty$. Following a Leray's point of view, roughly speaking our result proves that a possible space-time turbulence does not perturb the asymptotic spatial behavior of the initial data of a suitable weak solution

Global L^r-estimates and regularizing effect for solutions to the p(t, x) -Laplacian systems

We consider the initial boundary value problem for the p(t, x)-Laplacian system in a bounded domain \Omega. If the initial data belongs to L^{r_0}, r_0 \geq 2, we give a global L^{r_0}({\Omega})-regularity result uniformly in t>0 that, in the particular case r_0 =\infty, implies a maximum modulus theorem. Under the assumption p- = \inf p(t, x) > 2n/(n+r_0), we also state L^{r_0}- L^r estimates for the solution, for r \geq r_0. Complete proofs of the results presented here are given in the paper [F. Crispo, P. Maremonti, M. Ruzicka, Global L^r-estimates and regularizing effect for solutions to the p(t, x) -Laplacian systems, accepted for publication on Advances in Differential Equations, 2017]

Singular p-Laplacian parabolic system in exterior domains: higher regularity of solutions and related properties of extinction and asymptotic behavior in time

We consider the IBVP in exterior domains for the p-Laplacian parabolic system. We prove regularity up to the boundary, extinction properties for p \in ( 2n/(n+2) , 2n/(n+1) ) and exponential decay for p= 2n/(n+1)

On the high regularity of solutions to the p-Laplacian boundary value problem in exterior domains

In this note, we consider the boundary value problem in exterior domains for the p-Laplacian system, p ∈ (1, 2). For suitable p and Lr -spaces, r > n, we furnish existence of a high-regular solution that is a solution whose second derivatives belong to L r (Ω ). Hence, in particular we get λ-Hölder continuity of the gradient of the solution, with λ = 1 − n/r Further, we improve previous results on W2,2-regularity in a bounded domain

Dexamethasone sensitizes to ferroptosis by glucocorticoid receptor-induced dipeptidase-1 expression and glutathione depletion

Dexamethasone is widely used as an immunosuppressive therapy and recently as COVID-19 treatment. Here, we demonstrate that dexamethasone sensitizes to ferroptosis, a form of iron-catalyzed necrosis, previously suggested to contribute to diseases such as acute kidney injury, myocardial infarction, and stroke, all of which are triggered by glutathione (GSH) depletion. GSH levels were significantly decreased by dexamethasone. Mechanistically, we identified that dexamethasone up-regulated the GSH metabolism regulating protein dipeptidase-1 (DPEP1) in a glucocorticoid receptor (GR)-dependent manner. DPEP1 knockdown reversed the phenotype of dexamethasone-induced ferroptosis sensitization. Ferroptosis inhibitors, the DPEP1 inhibitor cilastatin, or genetic DPEP1 inactivation reversed the dexamethasone-induced increase in tubular necrosis in freshly isolated renal tubules. Our data indicate that dexamethasone sensitizes to ferroptosis by a GR-mediated increase in DPEP1 expression and GSH depletion. Together, we identified a previously unknown mechanism of glucocorticoid-mediated sensitization to ferroptosis bearing clinical and therapeutic implications

Gasdermin D-deficient mice are hypersensitive to acute kidney injury

Signaling pathways of regulated necrosis, such as necroptosis and ferroptosis, contribute to acute kidney injury (AKI), but the role of pyroptosis is unclear. Pyroptosis is mediated by the pore-forming protein gasdermin D (GSDMD). Here, we report a specific pattern of GSDMD-protein expression in the peritubular compartment of mice that underwent bilateral ischemia and reperfusion injury (IRI). Along similar lines, the GSDMD-protein expression in whole kidney lysates increased during the first 84 h following cisplatin-induced AKI. Importantly, unlike whole kidney lysates, no GSDMD-protein expression was detectable in isolated kidney tubules. In IRI and cisplatin-induced AKI, GSDMD-deficient mice exhibited hypersensitivity to injury as assessed by tubular damage, elevated markers of serum urea, and serum creatinine. This hypersensitivity was reversed by a combined deficiency of GSDMD and the necroptosis mediator mixed lineage kinase domain-like (MLKL). In conclusion, we demonstrate a non-cell autonomous role for GSDMD in protecting the tubular compartment from necroptosis-mediated damage in IRI

vPIF-1 is an insulin-like antiferroptotic viral peptide

Iridoviridae, such as the lymphocystis disease virus-1 (LCDV-1) and other viruses, encode viral insulin-like peptides (VILPs) which are capable of triggering insulin receptors (IRs) and insulin-like growth factor receptors. The homology of VILPs includes highly conserved disulfide bridges. However, the binding affinities to IRs were reported to be 200- to 500-fold less effective compared to the endogenous ligands. We therefore speculated that these peptides also have noninsulin functions. Here, we report that the LCDV-1 VILP can function as a potent and highly specific inhibitor of ferroptosis. Induction of cell death by the ferroptosis inducers erastin, RSL3, FIN56, and FINO2 and nonferroptotic necrosis produced by the thioredoxin-reductase inhibitor ferroptocide were potently prevented by LCDV-1, while human insulin had no effect. Fas-induced apoptosis, necroptosis, mitotane-induced cell death and growth hormone-releasing hormone antagonist-induced necrosis were unaffected, suggesting the specificity to ferroptosis inhibition by the LCDV-1 VILP. Mechanistically, we identified the viral C-peptide to be required for inhibition of lipid peroxidation and ferroptosis inhibition, while the human C-peptide exhibited no antiferroptotic properties. In addition, the deletion of the viral C-peptide abolishes radical trapping activity in cell-free systems. We conclude that iridoviridae, through the expression of insulin-like viral peptides, are capable of preventing ferroptosis. In analogy to the viral mitochondrial inhibitor of apoptosis and the viral inhibitor of RIP activation (vIRA) that prevents necroptosis, we rename the LCDV-1 VILP a viral peptide inhibitor of ferroptosis-1. Finally, our findings indicate that ferroptosis may function as a viral defense mechanism in lower organisms