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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

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To link to this item 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
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:78828
Publisher:Springer

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