Generalised vectorial ∞-eigenvalue non linear problems for L∞ functionals

Katzourakis, N. (2022) Generalised vectorial ∞-eigenvalue non linear problems for L∞ functionals. Nonlinear Analysis: Theory, Methods & Applications, 219. 112806. ISSN 0362-546X doi: 10.1016/j.na.2022.112806

Abstract/Summary

Let Ω R n , f ∈ C 1 (R N ×n) and g ∈ C 1 (R N), where N, n ∈ N. We study the minimisation problem of finding u ∈ W 1,∞ 0 (Ω; R N) that satisfies f (Du) L ∞ (Ω) = inf f (Dv) L ∞ (Ω) : v ∈ W 1,∞ 0 (Ω; R N), g(v) L ∞ (Ω) = 1 , under natural assumptions on f, g. This includes the ∞-eigenvalue problem as a special case. Herein we prove the existence of a minimiser u∞ with extra properties, derived as the limit of minimisers of approximating constrained L p problems as p → ∞. A central contribution and novelty of this work is that u∞ is shown to solve a divergence PDE with measure coefficients, whose leading term is a divergence counterpart equation of the non-divergence ∞-Laplacian. Our results are new even in the scalar case of the ∞-eigenvalue problem.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/102539
Identification Number/DOI	10.1016/j.na.2022.112806
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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