Preprint
Inserted: 24 jul 2025
Last Updated: 24 jul 2025
Year: 2025
Abstract:
We prove higher integrability for local minimizers of the double-phase orthotropic functional
\[
\sum_{i=1}^{n} \int_\Omega \bigg( \
u_{x_i}\
^{p} + a(x) \
u_{x_i} \
^{q} \bigg)dx
\]
when the weight function $a \geq0$ is assumed to be $\alpha$-Hölder continuous, while the exponents $p, q$ are such that $2 \leq p \leq q$ and $\frac{q}{p} < 1 + \frac{\alpha}{n}$. Under natural Sobolev regularity of~$a$, we further obtain explicit Lipschitz regularity estimates for local minimizers.
Download: