Existence, uniqueness and structure of second order absolute minimisers

Nikos Katzourakis, Roger Moser

Research output: Contribution to journalArticle

5 Citations (Scopus)
59 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)1615-1634
Number of pages20
JournalArchive for Rational Mechanics and Analysis
Volume231
Issue number3
Early online date6 Sep 2018
DOIs
Publication statusPublished - 1 Mar 2019

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