On the well-posedness of a two-phase minimization problem

• Author(s): Urbano, José Miguel ; Vorotnikov, Dmitry
• Date: 2010
• Persistent ID: http://hdl.handle.net/10316/13715
• Origin: Estudo Geral - Universidade de Coimbra
• Subject(s): In finity Laplacian; Viscosity solutions; Geometric properties of Sobolev functions
• Document Type: Preprint
• Language: English

Description

We prove a series of results concerning the emptiness and non-emptiness of a certain set of Sobolev functions related to the well-posedness of a two-phase minimization problem, involving both the p(x)-norm and the in nity norm. The results, although interesting in their own right, hold the promise of a wider applicability since they can be relevant in the context of other problems where minimization of the p-energy in a part of the domain is coupled with the more local minimization of the L1-norm on another region