We consider a class of Dirichlet boundary problems for nonlinear elliptic equations with a first order term. We show how the summability of the gradient of a solution increases when the summability of the datum increases. We also prove comparison principle which gives in turn uniqueness results by strenghtening the assumptions on the operators.

In this article we consider the following problem with max{p − 1, 1} ≤ q ≤ p < N, Ω a bounded domain and f, g positive measurable functions in Ω. We give assumptions on g with respect to q and p for which for all λ > 0 and all f ∈ L ¹ (Ω), f ≥ 0, problem (P) has a positive solution. In particular, we focus our attention on the case when 0 ∈ Ω and to prove that the assumptions on g are optimal. Furthermore, regularity results are given.

Inclusive computational practices are increasingly being employed to enrich knowledge and facilitate sensemaking in STEM education. Embedding computational activities in Computer-Supported Collaborative Learning environments can enhance students’ experiences. This study aimed to investigate the knowledge co-construction process within tailored student-led computational lab activities designed for a Computational Finance module. In particular, this study focused on the analysis of the effects of different lab practices and of group composition on knowledge co-construction. The groups designed for the lab activities were internally homogenous in terms of student ability. The sample consisted of 396 answers to a weekly survey filled out by all 50 of the undergraduate students who attended the module during the AY 2020/2021. The qualitative analysis relied on an adapted version of the Interaction Analysis Model designed by Gunawardena and colleagues for collaborative knowledge construction. Quantitative analyses were then conducted to study how the different lab practices and the composition of the groups affected the interaction. The findings revealed that, although the lower phases were the most prevalent, significant negotiations of meaning and discussions were activated, especially in tasks guiding towards sensemaking. Furthermore, the groups composed of lower-achieving students were the most engaged in negotiating and improving understanding as a result of the group interaction.