arXiv subjects

Anna Balci

Publications and source records attributed to Anna Balci.

5 recordsLinked to original sources

arXiv2026

Gradient estimates for $p\left(\cdot\right)$-harmonic differential forms

In this paper, we establish gradient bounds for $p(\cdot)$-harmonic differential forms subject to a Coulomb-type gauge condition. For variable exponents satisfying the log-H\"older continuity assumption, we derive higher integrability estimates of Meyers type, ensuring improved regularity beyond the natural energy space. Furthermore, under the stronger assumption of H\"older continuity of the exponent function, we prove that the gradient of solutions exhibits H\"older continuity. These results extend classical regularity theory for constant-exponent $p$-harmonic systems to the variable-exponent setting, which is essential for modeling nonhomogeneous and anisotropic media.

math.AP↗

arXiv2025

Hodge Decomposition and Potentials in Variable Exponent Lebesgue and Sobolev Spaces

The objective of this work is to establish a systematic study of boundary value problems within the framework of differential forms and variable exponent spaces. Specifically, we investigate the Hodge Laplacian and related first order systems like the div-curl systems, Hodge-Dirac systems, and Bogovskii-type problems in the context of variable exponent spaces. Our approach yields both existence theorems and elliptic estimates. These estimates provide key results such as the Hodge decomposition theorem, Gaffney inequality, and gauge fixing. These findings are crucial for advancing the nonlinear theory related to problems involving differential forms.

math.AP↗

arXiv2025

Examples of $p$-harmonic maps

We construct explicit examples of $p$-harmonic maps $u:\mathbb{R}^n \to \mathbb{R}^N$. These are more irregular than the previously known examples and thus provide new upper bounds for the regularity of $p$-harmonic maps, including the case of $\infty$-harmonic maps. To optimize our approach, we utilize solutions of the Hurwitz problem from algebra.

math.AP↗

arXiv2023

Scalar minimizers with maximal singular sets and lack of Meyers property

We present a general procedure to construct examples of convex scalar variational problems which admit a minimizers with large singular sets. The dimension of the set of singularities is maximal and the minimizer has no higher integrability property (failure of Meyers property).

math.AP↗

arXiv2023

Nonlocal and mixed models with Lavrentiev Gap

We present a general framework for constructing examples on Lavrentiev energy gap for nonlocal problems and apply it to several nonlocal and mixed models of double-phase type.

math.AP↗