University of Birmingham > Talks@bham > Analysis Seminar > Higher order L∞ variational problems and the ∞-Polylaplacian

Higher order L∞ variational problems and the ∞-Polylaplacian

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If you have a question about this talk, please contact Andrew Morris.

Calculus of Variations in L∞ is a relatively new field initiated by Aronsson in the 1960s which is under active research since. Minimising a “maximum energy” is very challenging because the resulting functional is non-local and the equations arising as the analogues of the Euler-Lagrange equations are non-divergence, highly nonlinear and degenerate. However, the L∞ approach furnishes more realistic models than the classical average functionals (integrals). In this talk I will discuss recent advances on the study of 2nd order variational problems in L∞ seeking to minimise an energy involving second derivatives. This problem is partly motivated by curvature minimisation problems in Riemannian Geometry and by Data Assimilation questions. We also derived and studied the associated PDE which is fully nonlinear and of 3rd order. Our analysis relies on the recently proposed theory of D-solutions, a general duality-free approach of generalised solutions for fully nonlinear PDE systems which do not support integration-by-parts.

This talk is part of the Analysis Seminar series.

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