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

Elisa Calzolari; Roberta Filippucci; Patrizia Pucci

doi:10.3934/proc.2007.2007.191

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2007, Volume 2007: 191-200. Doi: 10.3934/proc.2007.2007.191 open access

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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: August 31, 2006

Revised: May 31, 2007

Published: August 2007

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Abstract

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].

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Mathematics Subject Classification: Primary, 35 J 15, Secondary, 35 J 70.

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