Existence, uniqueness and structure of second order absolute minimisers

Katzourakis, N. and Moser, R. (2019) Existence, uniqueness and structure of second order absolute minimisers. Archive for Rational Mechanics and Analysis, 231 (3). pp. 1615-1634. ISSN 0003-9527 doi: 10.1007/s00205-018-1305-6

Abstract/Summary

Let ⊆ 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(·, u)L∞(O), O ⊆ measurable, with prescribed boundary conditions for u and Du on ∂ and under natural assumptions on F. We also show that u∞ is partially smooth and there exists a harmonic function f∞ ∈ L1() such that F(x, u∞(x)) = e∞ sgn f∞(x) for all x ∈ { f∞ = 0}, where e∞ is the infimum of the global energy.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/78828
Identification Number/DOI	10.1007/s00205-018-1305-6
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
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