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math.AP2026
Harnack inequality for double-phase functionals with Muckenhoupt-type growth functions
Minh-Phuong Tran, Thanh-Nhan Nguyen
We investigate a general class of variational integrals under a structural condition imposed on the double-phase function, recently introduced in~\cite{ADKO2026}. In this setting,…
math.AP2026
Revisiting multi-phase variational problems: A Muckenhoupt weight approach
Thanh-Nhan Nguyen, Minh-Phuong Tran
In this paper, we investigate the regularity theory of local minimizers of multi-phase energy functionals. As a key feature of our work, instead of the classical Hölder continuity…
math.AP2026
Global regularity estimates for -Laplacian variational inequalities with singular or degenerate matrix-valued weights
Minh-Phuong Tran, Duc-Quang Bui, Thanh-Nhan Nguyen
We establish the global gradient bounds for weak solutions to the elliptic variational inequality with two-sided obstructions, associated with a -Laplacian type operator invo…