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We study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval I, under Dirichlet conditions in the exterior of I. This model is strictly related to the mathematical description of galvanic corrosion phenomena for simple electrochemical systems. By means of the finite-dimensional Lyapunov–Schmidt reduction method, we construct bubbling families of solutions developing an arbitrarily prescribed number sign-alternating peaks. With a careful analysis of the limit profile of the solutions, we also show that the number of nodal regions coincides with the number of blow-up points.

We prove the existence of extremals for fractional Moser–Trudinger inequalities in an interval and on the whole real line. In both cases we use blow-up analysis for the corresponding Euler–Lagrange equation, which requires new sharp estimates obtained via commutator techniques.

We extend the Moser–Trudinger inequality

We study the metrics of constant |$Q$| -curvature in the Euclidean space with a prescribed singularity at the origin, namely solutions to the equation $$\begin{equation*} (-\Delta)^{\frac{n}{2}}w=e^{nw}-c\delta_{0} \ \textrm{on}\ {\mathbb{R}}^n, \end{equation*}$$ under a finite volume condition. We analyze the asymptotic behavior at infinity and the existence of solutions for every |$n\ge 3$| also in a supercritical regime. Finally, we state some open problems. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of an extremal function for the Adams–Moser–Trudinger inequality on the Sobolev space H 0 m (Ω) , where Ω is any bounded, smooth, open subset of ℝ 2 m , m ≥ 1. Moreover, we extend this result to improved versions of Adams' inequality of Adimurthi-Druet type. Our strategy is based on blow-up analysis for sequences of subcritical extremals and introduces several new techniques and constructions. The most important one is a new procedure for obtaining capacity-type estimates on annular regions. [ABSTRACT FROM AUTHOR]

Biomethane potential from the anaerobic digestion of rice straw, hazelnut skin, and cocoa bean shell was investigated after applying an organosolv pretreatment. Pretreatment of the three lignocellulosic materials was performed at 150°C and 180°C for 60 min using 50% (v/v) ethanol as organic solvent. Afterward, untreated and pretreated feedstocks were used in batch biomethane production tests under mesophilic conditions (37 ± 1°C). The highest efficiency was obtained pretreating the rice straw at 180°C, which resulted in a 42% higher biomethane production yield from the 235 mL CH4/g volatile solid obtained with the untreated straw. A lower increase was achieved for hazelnut skin, whereas a partial inhibition of the biomethane production was observed for cocoa bean shell, compared with untreated materials. Compositional analyses showed that, after organosolv pretreatment, a reduction of the lignin and hemicellulose content was achieved in the three lignocellulosic residues, together with a relative increase of cellulose content. [ABSTRACT FROM AUTHOR]

We study Moser–Trudinger type functionals in the presence of singular potentials. In particular we propose a proof of a singular Carleson–Chang type estimate by means of Onofri’s inequality for the unit disk in R 2 . Moreover we extend the analysis of Adimurthi (2004) and Csató and Roy (2015a) considering Adimurthi–Druet type functionals on compact surfaces with conical singularities and discussing the existence of extremals for such functionals. [ABSTRACT FROM AUTHOR]

This study investigated effects of chemical pretreatment with N-methylmorpholine-N-oxide (NMMO) on methane yields of rice straw, cocoa bean shell, and hazelnut skin. Three lignocellulosic materials were separately pretreated with NMMO at 120°C for 3 h. Subsequently, batch biomethane production tests were performed under mesophilic (37°C - 2°C) conditions, also with the untreated feedstocks, to provide methane production baseline data. Pretreatment was particularly effective for rice straw, with an 82% increased biomethane production yield from 206mL CH4/g volatile solids (VS) obtained with the untreated substrate. A lower enhancement of the biomethane yield from 199 to 226mL CH4/g VS (i.e., 14% increase) was observed for cocoa shell. For hazelnut skin, NMMO pretreatment resulted in a faster digestion rate in the initial 7 days, increasing the biomethane yield from 17 to 27mL CH4/g VS$day. However, the cumulative biomethane yield after 40 days was not affected by NMMO pretreatment. [ABSTRACT FROM AUTHOR]

We establish uniform a-priori estimates for solutions of the semilinear Dirichlet problem (− Δ) m u = h (x , u) in Ω , u = ∂ n u = ⋯ = ∂ n m − 1 u = 0 on ∂ Ω , where h is a positive superlinear and subcritical nonlinearity in the sense of the Trudinger–Moser–Adams inequality, either when Ω is a ball or, provided an energy control on solutions is prescribed, when Ω is a smooth bounded domain. Our results are sharp within the class of distributional solutions. The analogous problem with Navier boundary conditions is also studied. Finally, as a consequence of our results, existence of a positive solution is shown by degree theory. [ABSTRACT FROM AUTHOR]

Rice straw is an abundant and sustainable substrate for anaerobic digestion (AD), but it is often deficient in essential trace elements (TEs) for proper microbial growth and metabolism. A lack of TEs leads to AD imbalances and suboptimal biogas yields. However, the total TE concentration is not a sufficient indicator of the amount of TEs available to the microorganisms. Therefore, this study investigated the degree of bioavailability of iron (Fe) and cobalt (Co) during the AD of rice straw, and correlated it to the biomethane yields and volatile fatty acids (VFAs) produced. When the two TEs were dosed at 205 µg Fe/g TS and 18 µg Co/g TS of rice straw, the biomethane production was approximately 260 mL CH4/g VS, i.e., similar to that obtained when Fe and Co were not added. Despite an increased bioavailable fraction of 23 and 48% for Fe and Co, respectively, after TEs addition, the AD performance was not enhanced. Moreover, VFAs did not exceed 250 mg HAc/L both in the presence and absence of added TEs, confirming no enhancement of the methanogenesis step. Therefore, the bioavailability of Fe and Co was not a limiting factor for the biomethane production at low total VFAs concentration. [ABSTRACT FROM AUTHOR]