On the regularity of minimizers for scalar integral functionals with $(p,q)$-growth

Abstract

We revisit the question of regularity for minimizers of scalar autonomous integral functionals with so-called $(p,q)$-growth. In particular, we establish Lipschitz regularity under the condition $\frac{q}{p}<1+\frac{2}{n-1}$ for $n\ge 3$ which improves a classical result due to Marcellini~[JDE'91].

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• Regularity theory for non-autonomous partial differential equations without Uhlenbeck structure
• On a range of exponents for absence of Lavrentiev phenomenon for double phase functionals
• Regularity theory for non-autonomous problems with a priori assumptions
• Global higher integrability for minimisers of convex obstacle problems with (p,q)-growth
• Regularity for multi-phase problems at nearly linear growth
• Quantitative nonlinear homogenization: control of oscillations
• Lipschitz bounds for nonuniformly elliptic integral functionals in the plane
• Higher integrability for variational integrals with non-standard growth