Submitted Paper
Inserted: 5 jan 2024
Last Updated: 1 mar 2024
Year: 2024
Abstract:
Minima of the log-multiphase variational integral
$
w \mapsto \int_{\Omega} [
Dw
\log(1+
Dw
) + a(x)
Dw
^q + b(x)
Dw
^s] \, {\rm d}x\,,
$
have locally Hölder continuous gradient under sharp quantitative bounds linking the growth powers $(q,s)$ to the Hölder exponents of the modulating coefficients $a(\cdot)$ and $b(\cdot)$ respectively.
Keywords: regularity, Nearly linear growth, nonuniform ellipticity
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