What question did this study set out to answer?

The research aims to identify conditions under which closed sets are removable for α-Hölder continuous A-harmonic functions in a reversible Finsler manifold.

March 13, 2026Nonlinear Differential Equations and Applications NoDEA0 citationsOpen Access

Removable sets for Hölder continuous solutions of A-harmonic functions on Finsler manifolds

JAJuan Pablo Alcon Apaza

Key Points

The research aims to identify conditions under which closed sets are removable for α-Hölder continuous A-harmonic functions in a reversible Finsler manifold.
Analyzed closed sets in relation to a specific type of A-harmonic function.
Examined Hausdorff measure dimensions within the context of removable sets.
Considered assumptions on the Finsler manifold and variable exponents.
Established that closed sets are removable under defined conditions and dimensional assumptions.
Identified specific cases where the Hausdorff measure equals zero, implying removability.
Provided estimates for measures of balls in the Finsler manifold setting.

Abstract

Abstract We show that a closed set S S is removable for α -Hölder continuous A A -harmonic functions in a domain Ω within a reversible Finsler manifold (M, F, V) (M, F, V) of dimension n 2 n ≥ 2. This removability holds under certain assumptions on (M, F, V) (M, F, V) and the variable exponent p, provided that for every compact subset K S K ⊂ S, the Hausdorff measure of K with dimension n₁ - pK^+ + (pK^+ - 1) n 1 - p K + + α (p K + - 1) is zero. Here, pK^+ = K p p K + = sup K p, and n₁ n 1 is a dimension exponent satisfying the growth condition V (B (x, r) ) Kr^ {n₁} V (B (x, r) ) ≤ K r n 1 for all balls. The second main result establishes an estimate for (B (x, r) ): = \{ ₁ (ₗ, ₑ)

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