TY - JOUR
T1 - Convex integration with linear constraints and its applications
AU - Kim, Seonghak
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/7/15
Y1 - 2020/7/15
N2 - We study solutions of the first order partial differential inclusions of the form ∇u∈K, where u:Ω⊂Rn→Rm and K is a set of m×n real matrices, and derive a companion version to the result of Müller and Šverák [16], concerning a general linear constraint on the components of ∇u. We then consider two applications: the vectorial eikonal equation and a T4-configuration both under linear constraints.
AB - We study solutions of the first order partial differential inclusions of the form ∇u∈K, where u:Ω⊂Rn→Rm and K is a set of m×n real matrices, and derive a companion version to the result of Müller and Šverák [16], concerning a general linear constraint on the components of ∇u. We then consider two applications: the vectorial eikonal equation and a T4-configuration both under linear constraints.
KW - Baire's category method
KW - Convex integration
KW - Linear constraints
KW - Partial differential inclusions
KW - T-configuration
KW - Vectorial eikonal equation
UR - http://www.scopus.com/inward/record.url?scp=85081230047&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2020.124028
DO - 10.1016/j.jmaa.2020.124028
M3 - Article
AN - SCOPUS:85081230047
SN - 0022-247X
VL - 487
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 124028
ER -