Variational problems in L∞ involving semilinear second order differential operators

Katzourakis, N. and Moser, R. (2023) Variational problems in L∞ involving semilinear second order differential operators. ESAIM Control Optimization & Calculus of Variations, 29. 76. ISSN 1262-3377 doi: 10.1051/cocv/2023066

Abstract/Summary

For an elliptic, semilinear differential operator of the form S(u) = A : D2u + b(x, u, Du), consider the functional E∞(u) = ess supΩ, |S(u)|. We study minimisers of E∞ for prescribed boundary data. Because the functional is not differentiable, this problem does not give rise to a conventional Euler-Lagrange equation. Under certain conditions, we can nevertheless give a system of partial differential equations that all minimisers must satisfy. Moreover, the condition is equivalent to a weaker version of the variational problem. The theory of partial differential equations therefore becomes available for the study of a large class of variational problems in L∞ for the first time.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/115739
Identification Number/DOI	10.1051/cocv/2023066
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	EDP Sciences
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