Regularity for minimizers of integrals with nonstandard growth. (English) Zbl 1327.49064
Summary: We deal with variational integrals
\[
\int_\Omega f(x, D u(x)) dx
\]
and we consider a minimizer \(u \colon \Omega \subset \mathbb{R}^n \to \mathbb{R}\) among all functions that agree on the boundary \(\partial \Omega\) with some fixed boundary value \(u_\ast\). We assume that the boundary datum \(u_\ast\) makes the density \(f(x, D u_\ast(x))\) more integrable and we prove that the minimizer \(u\) enjoys higher integrability.
MSC:
| 49N60 | Regularity of solutions in optimal control |
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