Existence, unique continuation and symmetry of least energy nodal solutions to sublinear Neumann problems

We consider the sublinear problem \begin {equation*} \left\{\begin{array}{r c l c} -\Delta u & = &|u|^{q-2}u & \textrm{in }\Omega, \\ u_n & = & 0 & \textrm{on }\partial\Omega,\end{array}\right. \end {equation*} where $\Omega \subset \real^N$ is a bounded domain, and $1 \leq q < 2$. For $q=1$, $|u|^{q-2}u$ will be identified with \sgn(u). We establish a variational principle for least energy nodal solutions, and we investigate their qualitative properties. In particular, we show that they satisfy a unique continuation property (their zero set is Lebesgue-negligible). Moreover, if $\Omega$ is radial, then least energy nodal solutions are foliated Schwarz symmetric, and they are nonradial in case $\Omega$ is a ball. The case $q=1$ requires special treatment since the formally associated energy functional is not differentiable, and many arguments have to be adjusted

The fractional Cheeger problem

Given an open and bounded set $\Omega\subset\mathbb{R}^N$, we consider the problem of minimizing the ratio between the $s-$perimeter and the $N-$dimensional Lebesgue measure among subsets of $\Omega$. This is the nonlocal version of the well-known Cheeger problem. We prove various properties of optimal sets for this problem, as well as some equivalent formulations. In addition, the limiting behaviour of some nonlinear and nonlocal eigenvalue problems is investigated, in relation with this optimization problem. The presentation is as self-contained as possible.Comment: 33 pages, 2 figure

Does Bridget Jones watch EastEnders or The Love Boat? Cultural and linguistic issues in the translation of chick-lit novels

Abstract - Chick lit is a genre comprised of books chiefly written by women for women. These books are mainly characterized by the tone, which is very confidential and personal, and often relies on the use of colloquial and slangy (and occasionally obscene) expressions, by the use of humour, and by the numerous references to popular culture. This paper aims at analyzing the strategies used in the Italian translation of one of the best-known examples of the genre, Helen Fielding’s Bridget Jones’s Diary, taking two frames of reference. First of all, the analysis will try to identify in the target text the distinctive universal features observed in computer-based corpus translation (Baker 1996), namely explicitation, simplification and normalization. Secondly, it will consider the translation in terms of Venuti’s dichotomy of translation strategies into domestication and foreignization (1995). Riassunto -Il chick lit è un genere letterario costituito principalmente da romanzi scritti perlopiù da autrici donne per un pubblico femminile. I romanzi chick-lit sono caratterizzati dal tono confidenziale e personale, dall’uso di espressioni colloquiali e slang (e occasionalmente volgari), dalla presenza costante di humour e dai numerosi riferimenti alla pop culture contemporanea. Questo saggio intende analizzare le strategie utilizzate nella traduzione italiana di uno degli esempi più rappresentativi del genere, ovvero Bridget Jones’s Diary di Helen Fielding, utilizzando due modelli di riferimento. Innanzitutto, lo studio tenterà di identificare la presenza degli universali traduttivi osservati nei corpus-based translation studies (Baker 1996), ovvero explicitation, simplification e normalization. Successivamente, si analizzerà la traduzione secondo la teoria delle strategie traduttive proposta da Venuti (1995), ovvero domestication e foreignization

Skiing Home at Dusk; The House Not Home; Solstice, Entering Capricorn

Jay Parini, who teaches at Middlebury College, is the author of several books including Anthracite Country (poems), and Theodore Roethke: An American Romantic

Asymptotic behaviour of higher eigenfunctions of the p-Laplacian as p goes to 1

Subject of this thesis is the asymptotic behaviour of the higher eigenvalues of the p-Laplacian operator as p goes to 1. The limit setting depends only on the geometry of the domain. In the particular case of a planar disc, it is possible to show that the second eigenfunctions are nonradial if p is close enough to 1. Moreover, it is shown that second eigenfunctions can be obtained as limit of least energy nodal solutions of a p-superlinear problem