TY - JOUR
T1 - Degenerate elliptic problems in a class of free domains
AU - Rodrigues, José Francisco
AU - Urbano, José Miguel
N1 - Generated from Scopus record by KAUST IRTS on 2023-02-15
PY - 1999/1/1
Y1 - 1999/1/1
N2 - We study a mixed boundary value problem for an operator of p-Laplacian type. The main feature of the problem is the fact that the exact domain where it is considered is not known a priori and is to be determined so that a certain integral condition is satisfied. We establish the existence of a unique solution to the problem, by means of the analysis of the range of an appropriate real function, and we show the continuous dependence with respect to a family of operators. These results can be applied to the study of unidirectional non-Newtonian flows of power-law type, in particular to solve a simplified problem arising in theoretical glaciology and to show the existence of a Bingham flow in an open channel; the uniqueness in this case is an open problem. © Elsevier, Paris.
AB - We study a mixed boundary value problem for an operator of p-Laplacian type. The main feature of the problem is the fact that the exact domain where it is considered is not known a priori and is to be determined so that a certain integral condition is satisfied. We establish the existence of a unique solution to the problem, by means of the analysis of the range of an appropriate real function, and we show the continuous dependence with respect to a family of operators. These results can be applied to the study of unidirectional non-Newtonian flows of power-law type, in particular to solve a simplified problem arising in theoretical glaciology and to show the existence of a Bingham flow in an open channel; the uniqueness in this case is an open problem. © Elsevier, Paris.
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021782499000173
UR - http://www.scopus.com/inward/record.url?scp=0033211583&partnerID=8YFLogxK
U2 - 10.1016/S0021-7824(99)00017-3
DO - 10.1016/S0021-7824(99)00017-3
M3 - Article
SN - 0021-7824
VL - 78
SP - 819
EP - 840
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
IS - 8
ER -