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 infinity 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 L∞-norm on another region. © 2011 Elsevier Inc.
|Original language||English (US)|
|Number of pages||10|
|Journal||Journal of Mathematical Analysis and Applications|
|State||Published - Jun 1 2011|
Bibliographical noteGenerated from Scopus record by KAUST IRTS on 2023-02-15
ASJC Scopus subject areas
- Applied Mathematics