Startseite On isosupremic vectorial minimisation problems in L ∞ with general nonlinear constraints
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On isosupremic vectorial minimisation problems in L ∞ with general nonlinear constraints

  • Ed Clark ORCID logo und Nikos Katzourakis EMAIL logo
Veröffentlicht/Copyright: 1. Juni 2023
Advances in Calculus of Variations
Aus der Zeitschrift Advances in Calculus of Variations Band 17 Heft 3

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.

Keywords: PDE-constrained optimisation; Euler–Lagrange equations; absolute minimisers; Aronsson–Euler systems; Kuhn–Tucker theory; isosupremic problems; isoperimetric problems
MSC 2020: 35J94; 49J20; 49K20; 49K35; 49K99; 35J92

Communicated by Juan Manfredi

Funding source: Engineering and Physical Sciences Research Council

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
Published in Print: 2024-07-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. A flow approach to the prescribed Gaussian curvature problem in ℍ𝑛+1
  3. A split special Lagrangian calibration associated with frame vorticity
  4. The homogeneous causal action principle on a compact domain in momentum space
  5. The Lp Minkowski problem for q-torsional rigidity
  6. A twist in sharp Sobolev inequalities with lower order remainder terms
  7. Least energy solutions for affine p-Laplace equations involving subcritical and critical nonlinearities
  8. Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains
  9. Existence of minimizers for the SDRI model in 2d: Wetting and dewetting regime with mismatch strain
  10. Generalized minimizing movements for the varifold Canham–Helfrich flow
  11. A characterization of gauge balls in ℍ n by horizontal curvature
  12. Minimizers of 3D anisotropic interaction energies
  13. Regularity results for a class of widely degenerate parabolic equations
  14. On isosupremic vectorial minimisation problems in L ∞ with general nonlinear constraints
  15. Quasiconformal, Lipschitz, and BV mappings in metric spaces
  16. Continuous differentiability of a weak solution to very singular elliptic equations involving anisotropic diffusivity
  17. Optimal transport with nonlinear mobilities: A deterministic particle approximation result
  18. On functions of bounded β-dimensional mean oscillation
  19. Relaxed many-body optimal transport and related asymptotics
  20. Minimizers of nonlocal polyconvex energies in nonlocal hyperelasticity
https://doi.org/10.1515/acv-2022-0068
Schlagwörter für diesen Artikel
PDE-constrained optimisation; Euler–Lagrange equations; absolute minimisers; Aronsson–Euler systems; Kuhn–Tucker theory; isosupremic problems; isoperimetric problems

Artikel in diesem Heft

  1. Frontmatter
  2. A flow approach to the prescribed Gaussian curvature problem in ℍ𝑛+1
  3. A split special Lagrangian calibration associated with frame vorticity
  4. The homogeneous causal action principle on a compact domain in momentum space
  5. The Lp Minkowski problem for q-torsional rigidity
  6. A twist in sharp Sobolev inequalities with lower order remainder terms
  7. Least energy solutions for affine p-Laplace equations involving subcritical and critical nonlinearities
  8. Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains
  9. Existence of minimizers for the SDRI model in 2d: Wetting and dewetting regime with mismatch strain
  10. Generalized minimizing movements for the varifold Canham–Helfrich flow
  11. A characterization of gauge balls in ℍ n by horizontal curvature
  12. Minimizers of 3D anisotropic interaction energies
  13. Regularity results for a class of widely degenerate parabolic equations
  14. On isosupremic vectorial minimisation problems in L ∞ with general nonlinear constraints
  15. Quasiconformal, Lipschitz, and BV mappings in metric spaces
  16. Continuous differentiability of a weak solution to very singular elliptic equations involving anisotropic diffusivity
  17. Optimal transport with nonlinear mobilities: A deterministic particle approximation result
  18. On functions of bounded β-dimensional mean oscillation
  19. Relaxed many-body optimal transport and related asymptotics
  20. Minimizers of nonlocal polyconvex energies in nonlocal hyperelasticity
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