arXiv subjects
Publications and source records attributed to Stefania Perrotta.
We consider a class of anisotropic energy integrals including fast and slow growth under a unified approach, proving that the local minimizers are locally Lipschitz continuous.
This paper is devoted to the study of an age-structured SIRS epidemic model, in which a population affected by a disease is divided into susceptible, infected, and removed individuals. We assume that the force of infection may be nonlinear and time-dependent. The model, originally introduced and studied by Iannelli and his co-authors, can be naturally formulated in an abstract setting and has traditionally been analyzed using fixed point techniques, most often the Banach contraction principle. Following the approaches of Inaba and Banasiak, our investigation is based on the semigroup theory, through which we study the existence of mild (integral) solutions. The main novelty of our work lies in the use of the topological degree for condensing maps instead of classical fixed-point arguments. We prove the existence of a unique, global, nonnegative solution to the model that satisfies the prescribed initial and nonlocal conditions and takes values in the space $L^1$ with respect to the age variable. Moreover, this solution depends continuously on the initial data.
We consider integral functionals with slow growth and explicit dependence on u of the lagrangian; this includes many relevant examples, as, for instance, in elastoplastic torsion problems or in image restoration problems. Our aim is to prove that the local minimizers are locally Lipschitz continuous. The proof makes use of recent results concerning the Bounded Slope Conditions.
We consider some energy integrals under slow growth and we prove that the local minimizers are locally Lipschitz continuous. Many examples are given, either with subquadratic $p,q-$growth and/or anisotropic growth.