Abstract
Let Ω⊆Rn be a bounded open C1,1 set. In this paper we prove the existence of a unique second order absolute minimiser u∞ of the functional
E∞(u,O):=∥F(⋅,Δu)∥L∞(O),O⊆Ωmeasurable,
with prescribed boundary conditions for u and Du on ∂Ω and under natural assumptions on F. We also show that u∞ is partially smooth and there exists a harmonic function f∞∈L1(Ω) such that
F(x,Δu∞(x))=e∞sgn(f∞(x))
for all x∈{f∞≠0} , where e∞ is the infimum of the global energy.
E∞(u,O):=∥F(⋅,Δu)∥L∞(O),O⊆Ωmeasurable,
with prescribed boundary conditions for u and Du on ∂Ω and under natural assumptions on F. We also show that u∞ is partially smooth and there exists a harmonic function f∞∈L1(Ω) such that
F(x,Δu∞(x))=e∞sgn(f∞(x))
for all x∈{f∞≠0} , where e∞ is the infimum of the global energy.
| Original language | English |
|---|---|
| Pages (from-to) | 1615-1634 |
| Number of pages | 20 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 231 |
| Issue number | 3 |
| Early online date | 6 Sept 2018 |
| DOIs | |
| Publication status | Published - 1 Mar 2019 |
