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math.AP2026
Gradient estimates for -harmonic differential forms
Anna Balci, Swarnendu Sil, Mikhail Surnachev
In this paper, we establish gradient bounds for -harmonic differential forms subject to a Coulomb-type gauge condition. For variable exponents satisfying the log-Hölder c…
math.AP2025
Hodge Decomposition and Potentials in Variable Exponent Lebesgue and Sobolev Spaces
Anna Balci, Swarnendu Sil, Mikhail Surnachev
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 i…
math.AP2023
Scalar minimizers with maximal singular sets and lack of Meyers property
Anna Balci, Lars Diening, Mikhail Surnachev
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 singularit…