TY - JOUR
T1 - Variational problems in L∞ involving semilinear second order differential operators
AU - Katzourakis, Nikos
AU - Moser, Roger
PY - 2023/10/11
Y1 - 2023/10/11
N2 - For an elliptic, semilinear differential operator of the form S(u)=A:D2u+b(x,u,Du), consider the functional E∞(u)=esssupΩ|S(u)|. We study minimisers of E∞ for prescribed boundary data. Because the functional is not differentiable, this problem does not give rise to a conventional Euler-Lagrange equation. Under certain conditions, we can nevertheless give a system of partial differential equations that all minimisers must satisfy. Moreover, the condition is equivalent to a weaker version of the variational problem.
AB - For an elliptic, semilinear differential operator of the form S(u)=A:D2u+b(x,u,Du), consider the functional E∞(u)=esssupΩ|S(u)|. We study minimisers of E∞ for prescribed boundary data. Because the functional is not differentiable, this problem does not give rise to a conventional Euler-Lagrange equation. Under certain conditions, we can nevertheless give a system of partial differential equations that all minimisers must satisfy. Moreover, the condition is equivalent to a weaker version of the variational problem.
U2 - 10.48550/arXiv.2303.15982
DO - 10.48550/arXiv.2303.15982
M3 - Article
SN - 1292-8119
VL - 29
JO - ESAIM: Control, Optimisation and Calculus of Variations
JF - ESAIM: Control, Optimisation and Calculus of Variations
M1 - 76
ER -