4 citations · 14 across the 24 of their papers we have counts for
21 papers · 1 filter
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,…
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…
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…
Calderón-Zygmund gradient estimates for -Laplace systems with BMO complex coefficients
Van-Chuong Quach, Thanh-Nhan Nguyen, Minh-Phuong Tran
This work is concerned with global gradient bounds for a class of divergence-form degenerate elliptic systems with complex-valued coefficients. Notably, the leading coefficients ar…
A large scaling property of level sets for degenerate -Laplacian equations with logarithmic BMO matrix weights
Thanh-Nhan Nguyen, Minh-Phuong Tran
In this study, we deal with generalized regularity properties for solutions to -Laplace equations with degenerate matrix weights. It has already been observed in previous intere…
Existence of weak solutions to borderline double-phase problems with logarithmic convection term
Minh-Phuong Tran, Thanh-Nhan Nguyen
In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic con…
Regularity for the steady Stokes-type flow of incompressible Newtonian fluids in some generalized function settings
Minh-Phuong Tran, Thanh-Nhan Nguyen, Hong-Nhung Nguyen
A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving -Laplacian is offered. The governing systems of equations are based on s…
Calderón-Zygmund-type estimates for singular quasilinear elliptic obstacle problems with measure data
Minh-Phuong Tran, Thanh-Nhan Nguyen, Phuoc-Nguyen Huynh
We deal with a global Calderón-Zygmund type estimate for elliptic obstacle problems of -Laplacian type with measure data. For this paper, we focus on the singular case of growth…
Lorentz gradient estimates for a class of elliptic p-Laplacian equations with a Schrödinger term
Minh-Phuong Tran, Thanh-Nhan Nguyen, Gia-Bao Nguyen
We prove in this paper the global Lorentz estimate in term of fractional-maximal function for gradient of weak solutions to a class of p-Laplace elliptic equations containing a non…
A global fractional Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data
Minh-Phuong Tran, Thanh-Nhan Nguyen
We prove a global fractional differentiability result via the fractional Caccioppoli-type estimate for solutions to nonlinear elliptic problems with measure data. This work is in f…
Weighted distribution approach to gradient estimates for quasilinear elliptic double-obstacle problems in Orlicz spaces
Thanh-Nhan Nguyen, Minh-Phuong Tran
We construct an efficient approach to deal with the global regularity estimates for a class of elliptic double-obstacle problems in Lorentz and Orlicz spaces. The motivation of thi…
Lorentz estimates for quasi-linear elliptic double obstacle problems involving a Schrödinger term
Thanh-Nhan Nguyen, Minh-Phuong Tran
Our goal in this article is to study the global Lorentz estimates for gradient of weak solutions to -Laplace double obstacle problems involving the Schrödinger term: $-Δ_p u + \…
Level-set inequalities on fractional maximal distribution functions and applications to regularity theory
Thanh-Nhan Nguyen, Minh-Phuong Tran
The aim of this paper is to establish an abstract theory based on the so-called fractional-maximal distribution functions (FMDs). From the rough ideas introduced in~\cite{AM2007},…
Lorentz improving estimates for the -Laplace equations with mixed data
Thanh-Nhan Nguyen, Minh-Phuong Tran
The aim of this paper is to develop the regularity theory for a weak solution to a class of quasilinear nonhomogeneous elliptic equations, whose prototype is the following mixed Di…
Global Lorentz estimates for non-uniformly nonlinear elliptic equations via fractional maximal operators
Thanh-Nhan Nguyen, Minh-Phuong Tran
This paper is a contribution to the study of regularity theory for nonlinear elliptic equations. The aim of this paper is to establish some global estimates for non-uniformly ellip…
An application of global gradient estimates in Lorentz-Morrey spaces: The existence of stationary solution to degenerate diffusive Hamilton-Jacobi equations
Minh-Phuong Tran, Thanh-Nhan Nguyen
In historical mathematics and physics, the Kardar-Parisi-Zhang equation or a quasilinear stationary version of a time-dependent viscous Hamilton-Jacobi equation in growing interfac…
Global gradient estimates for very singular quasilinear elliptic equations with measure data
Minh-Phuong Tran, Thanh-Nhan Nguyen
This paper continues the development of regularity results for quasilinear measure data problems \begin{align*} \begin{cases} -\mathrm{div}(A(x,\nabla u)) &= μ\quad \text{in} \ \ Ω…
Gradient estimates via Riesz potentials and fractional maximal operators for quasilinear elliptic equations with applications
Minh-Phuong Tran, Thanh-Nhan Nguyen
In this paper, the aim of our work is to establish global weighted gradient estimates via fractional maximal functions and the point-wise regularity estimates of Dirichlet problem…
New gradient estimates for solutions to quasilinear divergence form elliptic equations with general Dirichlet boundary data
Minh-Phuong Tran, T. -N. Nguyen
This paper studies a new gradient regularity in Lorentz spaces for solutions to a class of quasilinear divergence form elliptic equations with nonhomogeneous Dirichlet boundary con…
An endpoint case of the renormalization property for therelativistic Vlasov-Maxwell system
Minh-Phuong Tran, Thanh-Nhan Nguyen
Recently C. Bardos et al. presented in their fine paper \cite{Bardos} a proof of an Onsager type conjecture on renormalization property and the entropy conservation laws for the re…
Lorentz-Morrey global bounds for singular quasilinear elliptic equations with measure data
Minh-Phuong Tran, Thanh-Nhan Nguyen
The aim of this paper is to present the global estimate for gradient of renormalized solutions to the following quasilinear elliptic problem: \begin{align*} \begin{cases} -div(A(x,…