4 citations · 14 across the 24 of their papers we have counts for
25 papers
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…
A new approach to convergence analysis of iterative models with optimal error bounds
Minh-Phuong Tran, Thanh-Nhan Nguyen, Thai-Hung Nguyen +4
In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces.…
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,…
A remark on the interpolation inequality between Sobolev spaces and Morrey spaces
Minh-Phuong Tran, Thanh-Nhan Nguyen
Interpolation inequalities play an important role in the study of PDEs and their applications. There are still some interesting open questions and problems that related to integral…
Random walk in random environment, corrector equation, and homogenized coefficients: from theory to numerics, back and forth
A. -C. Egloffe, A. Gloria, J. -C. Mourrat +1
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analy…