Regularity for minimizers for functionals of double phase with variable exponents

Abstract

The functionals of double phase type \[ \mathcal{H} (u):= \int \left(|Du|^{p} + a(x)|Du|^{q} \right) dx, ( q > p > 1, a(x)\geq 0) \] are introduced in the epoch-making paper by Colombo-Mingione for constants $p$ and $q$, and investigated by them and Baroni. They obtained sharp regularity results for minimizers of such functionals. In this paper we treat the case that the exponents are functions of $x$ and partly generalize their regularity results.

Advances in nonlinear analysis

References in corpus (4)

• Double phase problems with variable growth
• Double-phase problems with reaction of arbitrary growth
• Multiple solutions of double phase variational problems with variable exponent
• Partial regularity of $p(x)$-harmonic maps

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• Combined effects of singular and superlinear nonlinearities in singular double phase problems in ${\mathbb{R}}^N$
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