ID 110918
Author
Content Type
Departmental Bulletin Paper
Description
Let L(u) = L(u,∇u) be a functional on W1,1(Ω) whose formal Euler-Lagrange equation at the critical point u of L is the prescribed mean curvature equation:

−div(∇u /√1 + |∇u|2)= g(x, u).

Suppose L(u) = L(u,Du) is a relaxed functional of L(u), the weakly lower semicontinuous extension of L on the space of functions of bounded variation. How dose the relaxation affect the prescribed mean curvature equation? Instead of an Euler-Lagrange equation, we obtain here the so-called Euler-Lagrange system of equations which the critical points u of L and their derivatives Du necessarily satisfy.
Journal Title
Journal of Mathematics
ISSN
13467387
NCID
AA11595324
Volume
50
Start Page
127
End Page
144
Sort Key
127
Published Date
2016
FullText File
language
eng
TextVersion
Publisher
departments
Science and Technology