Abstract
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) |
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Pages (from-to) | 159-168 |
Number of pages | 10 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 378 |
Issue number | 1 |
DOIs | |
State | Published - Jun 1 2011 |
Externally published | Yes |
ASJC Scopus subject areas
- Analysis
- Applied Mathematics