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

Pages: 191 - 200, Issue Special, September 2007

 Abstract        Full Text (220.8K)              

Elisa Calzolari - Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy (email)
Roberta Filippucci - Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy (email)
Patrizia Pucci - Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Via Vanvitelli 1, 06123 Perugia, Italy (email)

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].

Keywords:  Dead cores, p-Laplacian operator, weight functions.
Mathematics Subject Classification:  Primary, 35 J 15, Secondary, 35 J 70.

Received: September 2006;      Revised: June 2007;      Published: September 2007.