Regularity for multi-phase problems at nearly linear growth

Abstract

Minima of the log-multiphase variational integral $$w\mapsto {\int }_{\Omega }\left[|Dw|\log (1+|Dw|)+a(x)|Dw{|}^q+b(x)|Dw{|}^s\right]\mathrm{d}x,$$ 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.

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• Lipschitz bounds and nonautonomous integrals
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• Partial Regularity for BV Minimizers
• Regularity theory for non-autonomous partial differential equations without Uhlenbeck structure
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• Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth
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Cited by in corpus (3)

• Lipschitz bounds for nonuniformly elliptic integral functionals in the plane
• On the singular set of $\mathrm{BV}$ minimizers for non-autonomous functionals
• Local and global $C^{1,\beta }$-regularity for uniformly elliptic quasilinear equations of $p$-Laplace and Orlicz-Laplace type