TY - JOUR
T1 - On the well-posedness of a two-phase minimization problem
AU - Urbano, José Miguel
AU - Vorotnikov, Dmitry
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 2011/6/1
Y1 - 2011/6/1
N2 - 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.
AB - 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.
UR - https://linkinghub.elsevier.com/retrieve/pii/S0022247X1100031X
UR - http://www.scopus.com/inward/record.url?scp=79551688001&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2011.01.017
DO - 10.1016/j.jmaa.2011.01.017
M3 - Article
SN - 0022-247X
VL - 378
SP - 159
EP - 168
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -