Year: 2025
Type: preprint
Abstract: We consider the functional \[ F(u)=\int_Ω f(\nabla u)\,dx\qquad u\inφ+W^{1,1}_0(Ω) \] where $Ω$ is a Lipschitz bounded open set of $\R^N$, $f:\R^N\to\R\cup \{+\infty\}$ is a superlinear Borel function, $φ\in W^{1,\infty}(Ω)$. We prove that, if $f$ is superlinear and satisfies very weak assumptions, then the Lavrentiev phenomenon does not occur. We underline that our assumptions include the case of non continuous, non convex, and unbounded Lagrangians.
Source: arXiv (Cornell University)
Authors: Bertin, Tommaso, Treu, Giulia
Institution: University of Padua
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415965013
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