# American Institute of Mathematical Sciences

2007, 2007(Special): 191-200. doi: 10.3934/proc.2007.2007.191

## Dead cores and bursts for p-Laplacian elliptic equations with weights

 1 Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia

Received  September 2006 Revised  June 2007 Published  September 2007

In this paper we consider p-Laplace elliptic equations with weights on domains of $\mathbb{R}^n$, which include several prototypes, and we show that there exist a dead core solution having a burst within the core. This result is obtained by using an existence theorem for ground states having compact support, proved in [4] by the authors, together with qualitative properties and an existence theorem for dead core solutions contained in a recent work of Pucci and Serrin, see [10].
Citation: Elisa Calzolari, Roberta Filippucci, Patrizia Pucci. Dead cores and bursts for p-Laplacian elliptic equations with weights. Conference Publications, 2007, 2007 (Special) : 191-200. doi: 10.3934/proc.2007.2007.191
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