Sharp non-degenerate error theory for the full variable-exponent range

Establish sharp non-degenerate a priori error estimates for the Hybrid High-Order discretization of variable-exponent Leray–Lions problems across the full variable-exponent range, including the mixed and superquadratic regimes.

Background

The paper proves a regime-dependent optimal-order refinement only in the purely subquadratic case, where the essential supremum of the variable exponent satisfies p⁺ ≤ 2. Numerical experiments nevertheless observe optimal order k + 1 for smooth non-degenerate problems also in mixed and superquadratic regimes. The authors explicitly identify obtaining a sharp non-degenerate theory covering the entire variable-exponent range as an unresolved extension.