Work

Global Higher Integrability and Hardy Inequalities for Double-Phase Functionals under a Capacity Density Condition

Year: 2026

Type: article

Abstract: We prove global higher integrability for functionals of double-phase type under a uniform local capacity density condition on the complement of the considered domain $$\Omega \subset \mathbb {R}^n$$ . In this context, we investigate a new natural notion of variational capacity associated to the double-phase integrand. Under the related fatness condition for the complement of $$\Omega $$ , we establish an integral Hardy inequality. Further, we show that fatness of $$\mathbb {R}^n \setminus \Omega $$ is equivalent to a boundary Poincaré inequality, a pointwise Hardy inequality and to the local uniform p-fatness of $$\mathbb {R}^n \setminus \Omega $$ . We provide a counterexample that shows that the expected Maz’ya type inequality–a key intermediate step toward global higher integrability–does not hold with the notion of capacity involving the double-phase functional itself.

Source: Potential Analysis

DOI: 10.1007/s11118-026-10339-z

Authors: Fabian Bäuerlein, Leah Kurki Schätzler, Samuele Riccò

Institutions: University of Salzburg, University of Lisbon

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Austrian Science Fund, Universität Salzburg