Preprint

Inserted: 21 may 2025
Last Updated: 21 may 2025

Year: 2025

Abstract:

We prove a \(C^{1,1}\)-regularity of minimizers of the functional \[ \int_I \sqrt{1+\vert Du\vert ^2} + \int_I \vert u-g\vert\,ds,\quad u\in BV(I), \] provided \(I\subset\mathbb{R}\) is a bounded open interval and \(\vert\vert g\vert\vert_\infty\) is sufficiently small, thus partially establishing a De Giorgi conjecture in dimension one and codimension one. We also extend our result to a suitable anisotropic setting.

Tags: GeoMeG
Keywords: BV-functions, L^p-perturbation, anisotropic area functional, Cartesian area, De Giorgi conjecture

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• 1d_degiorgi_area.pdf