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On isosupremic vectorial minimisation problems in L with general nonlinear constraints

  • Ed Clark ORCID logo and Nikos Katzourakis EMAIL logo

Abstract

We study minimisation problems in L for general quasiconvex first order functionals, where the class of admissible mappings is constrained by the sublevel sets of another supremal functional and by the zero set of a nonlinear operator. Examples of admissible operators include those expressing pointwise, unilateral, integral isoperimetric, elliptic quasilinear differential, Jacobian and null Lagrangian constraints. Via the method of L p approximations as p , we illustrate the existence of a special L minimiser which solves a divergence PDE system involving certain auxiliary measures as coefficients. This system can be seen as a divergence form counterpart of the Aronsson PDE system which is associated with the constrained L variational problem.


Communicated by Juan Manfredi


Award Identifier / Grant number: GS19-055

Funding statement: E. Clark has been financially supported through the UK EPSRC scholarship GS19-055.

Acknowledgements

The authors would like to thank the referees of this paper for the careful reading of the manuscript and their constructive suggestions.

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Received: 2022-08-16
Accepted: 2023-03-10
Published Online: 2023-06-01

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